Journal of Nonlinear Modeling and Analysis
type: channel
description: The Journal of Nonlinear Modeling and Analysis (JNMA), started in 2019, aims to publish original research papers, communications as well as survey papers on theory and application of nonlinear analysis related to differential equations, dynamical systems and other areas in mathematics and mathematical sciences, including mathematical biology. The journal was published quarterly in March, June, September and December between 2019 and 2024. From 2025 on, it will be published bimonthly with its issues released in February, April, June, August, October and December.
publisher: Global Science Press
language: en
publication name: Journal of Nonlinear Modeling and Analysis
issn: 2562-2854
items: Global Attractors for the BBM Equation with Fading Memory
items: Steady State Solution and Its Stability Analysis of a Reaction-Diffusion Mathematical Model for LDL, Lipoprotein(a), and CRP in Atherosclerosis
items: Forced Epidemic Waves in a Nonlocal Dispersal SIR Model with Shifting Transmission and Time Delay
items: Solving the Kuramoto-Sivashinsky Equation via a Modified Adomian Decomposition Method
items: A Robust Fixed Point Method to Solve System of Nonlinear Equations
items: Homotopy Analysis Method on Listeria Infection Model Caused by Pre-Cooked Package Food
items: Numerical Solutions of Fuzzy Fractional Variable-Order Differential Equations
items: Stability Analysis of a Three-Dimensional Discrete Topp Model
items: On Constacyclic Codes of Length $4p^s$ over $F_{p^m}[u,v]/\langle u^2, v^2, uv-vu \rangle$
items: Solvability for a Class of Logarithmic Type Initial Conditions of Hadamard Fractional Differential System on an Infinite Interval
items: Dynamical Analysis of Virulence Evolution in Multistrain Infection Model Within Hosts
items: A Predator-Prey Biological Model of Multiple Species with Linear Growth Rates
items: Nonlinear Dynamics and Chaos in Fractional-Order Cardiac Action Potential Duration Mapping Model
items: A Semi-Analytical Study on SEIR Model with Vaccinated Effects
items: Geometric Inequality for CR-Slant Warped Product Submanifolds in Nearly Lorentzian Para-Sasakian Manifold
items: Dynamical Analysis in a Discrete Fractional Order Harvested Predator-Prey Model Incorporating Fear Effect and Refuge
items: Modelling Zika Virus, Dengue Fever and Chikungunya Virus: Gaining Insights into the Co-Dynamics of the Three Diseases
items: ESS in a River Network with Two Branches
items: Cross-Invariant Sets of the Cubic Nonlinear Schrödinger System with Partial Confinement
items: Analysis of a Fractional Order Eco-Epidemiological Model with Prey Infection and Predator Cannibalism
items: Optimal Control Approach for Bilateral Elastic Contact Problem with Power-Law Friction
items: Nonlinear Dynamics and Pull-in Phenomena in a Magneto-Electro MEMS Actuator with Hardening Spring
items: On the Numerical Solution of Solidification of Water
items: Generalized Variational Inclusion Problem Involving Averaged Operator and Cayley Operator
items: Stability Analysis of a Diffusive Ratio-Dependent Predator-Prey Model with Nonlocal Perception
items: The Impact of Educational Campaigns on the Global Dynamics of Cholera Epidemics
items: Existence Results for a Generalized $p$($x$)-Biharmonic Problem Type with No-Flux Boundary Condition
items: MEK Inhibition May Prevent the Recruitment of NK Cells in the Tumor Microenvironment: A Mathematical Model of Glioma Treatment
items: Local Ground-State and Mountain Pass Solutions for a $p$-Kirchhoff Equation with Critical Exponent
items: A Mathematical Modeling of Two-Strain Tuberculosis Transmission: Deterministic and Stochastic Approaches to Screening, Treatment, and Quarantine Strategies

Global Attractors for the BBM Equation with Fading Memory
type: item
description: This paper considers the existence of global attractors for BBM equation with fading memory. Using some new estimate technique to prove the existence of global attractors in topological space $H_1 × L^2_{\mu}(\mathbb{R}^+;H_1).$
subject: Articles
  topic: section
subject: BBM equations
  topic: keywords
subject: global attractors
  topic: keywords
subject: fading memory
  topic: keywords
creator: Dengjuan Feng
creator: Xiaobin Yao
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-14
publication date: 2026-04-14
starting page: 641
ending page: 647
doi: 10.12150/jnma.2026.641

Steady State Solution and Its Stability Analysis of a Reaction-Diffusion Mathematical Model for LDL, Lipoprotein(a), and CRP in Atherosclerosis
type: item
description: This study presents a reaction-diffusion mathematical model to investigate the spatiotemporal dynamics of low-density lipoprotein (LDL), lipoprotein(a), and C-reactive protein (CRP) within the arterial wall, key mediators in the pathogenesis of atherosclerosis and related cardiovascular diseases. The model employs a system of partial differential equations to capture both the diffusion of these biomolecules and their biochemical interactions, including LDL oxidation, CRP-mediated inflammatory responses, and plaque initiation. Numerical simulations, implemented using the finite difference method, demonstrate that CRP substantially accelerates LDL oxidation and promotes plaque deposition, particularly in regions of locally elevated lipoprotein concentrations. Furthermore, the results indicate that elevated CRP levels synergistically enhance the pro-atherogenic effects of LDL and lipoprotein(a), highlighting the critical role of inflammation in plaque progression. These findings underscore the potential of anti-inflammatory therapeutic strategies, alongside lipid-lowering interventions, in mitigating atherosclerotic risk. The proposed model provides a robust computational framework for elucidating the interactive effects of lipid metabolism and vascular inflammation in the progression of cardiovascular disease.
subject: Articles
  topic: section
subject: Finite difference
  topic: keywords
subject: reaction-diffusion
  topic: keywords
subject: LDL
  topic: keywords
subject: C-reactive protein (CRP)
  topic: keywords
subject: lipoprotein(a)
  topic: keywords
creator: Aytekin Enver
creator: Fatma Ayaz
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-13
publication date: 2026-04-13
starting page: 608
ending page: 640
doi: 10.12150/jnma.2026.608

Forced Epidemic Waves in a Nonlocal Dispersal SIR Model with Shifting Transmission and Time Delay
type: item
description: This paper is concerned with the forced epidemic waves of a nonlocal dispersal SIR model with shifting transmission and time delay. We first demonstrate that the existence of forced waves can be reduced to a fixed point problem. Then by constructing different pairs of upper and lower solutions and using Schauder's fixed point theorem, we establish two types of forced epidemic waves that reveal different state conversions of the disease. Moreover, we prove the nonexistence of forced epidemic waves when the basic reproduction number is less than unity. Finally, some biological explanations for the theoretical results are given in the discussion.
subject: Articles
  topic: section
subject: Forced waves
  topic: keywords
subject: shifting transmission
  topic: keywords
subject: nonlocal dispersal
  topic: keywords
subject: SIR model
  topic: keywords
subject: time delay
  topic: keywords
creator: Yilun Han
creator: Yan Li
creator: Jiabing Wang
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-13
publication date: 2026-04-13
starting page: 587
ending page: 607
doi: 10.12150/jnma.2026.587

Solving the Kuramoto-Sivashinsky Equation via a Modified Adomian Decomposition Method
type: item
description: The Kuramoto-Sivashinsky equation (KSE) is a well-known nonlinear partial differential equation (PDE) that plays a significant role in various scientific fields, particularly in fluid dynamics and reaction-diffusion systems. In this study, we employ the Modified Adomian Decomposition Method (MADM) to derive an analytical solution to the KSE over the domain $t \in \mathbb{R}$ and $0 \le x < 1$. The research provides a comprehensive analysis of the applicability of MADM in generating explicit series solutions for the KSE. The equation is formulated under proper initial conditions, and the systematic implementation of MADM is demonstrated involving the decomposition of nonlinear terms and successive approximation. The convergence and stability of the resulting series solutions are investigated, highlighting the method's efficiency in capturing the dynamics described by the KSE. Numerical simulations are presented to validate the analytical results, illustrating the effectiveness of the MADM in solving the KSE within the given parameters. This study not only enhances the theoretical understanding of the KSE but also serves as a practical guide for applying analytical techniques to complex nonlinear PDEs. Moreover, the proposed method represents a significant advancement in solving highly non-linear models by providing a straightforward recursive scheme that avoids linearization or small-parameter assumptions. The physical relevance of the obtained solutions is reflected in their ability to capture key features of instability and chaotic behavior characteristic of the KSE. These findings underscore the potential of MADM as a powerful and versatile tool in the study of spatiotemporal phenomena governed by nonlinear PDEs.
subject: Articles
  topic: section
subject: Non-linear evolution equations
  topic: keywords
subject: decomposition techniques
  topic: keywords
subject: series solutions
  topic: keywords
subject: initial value problems
  topic: keywords
creator: N. M. Dabwan
creator: Y. Q. Hasan
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-13
publication date: 2026-04-13
starting page: 570
ending page: 586
doi: 10.12150/jnma.2026.570

A Robust Fixed Point Method to Solve System of Nonlinear Equations
type: item
description: Solving nonlinear partial differential equations requires addressing systems of nonlinear algebraic equations. In this article, we propose a new fixed-point method for solving these systems. We assume that the method is both fast and globally convergent. Additionally, this method can be accelerated using Aitken or Anderson acceleration techniques. Several numerical test cases are presented to illustrate the efficiency of the proposed method.
subject: Articles
  topic: section
subject: Brouwer fixed point theorem
  topic: keywords
subject: system of equations
  topic: keywords
subject: global convergence
  topic: keywords
creator: M.R. Amattouch
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-13
publication date: 2026-04-13
starting page: 551
ending page: 569
doi: 10.12150/jnma.2026.551

Homotopy Analysis Method on Listeria Infection Model Caused by Pre-Cooked Package Food
type: item
description: In this study, the Listeria infection model involving the fractional derivatives in the Caputo sense is considered and studied through two different techniques called the Homotopy analysis method (HAM) and Runge-Kutta 4th order (RK4) method. HAM is a semi-analytical approach, and the RK4 method is a numerical method proposed for solving fractional order systems of ordinary differential equations (ODEs). We have developed a semi-analytical solution in terms of a series of polynomials by HAM and a numerical solution by the RK4 method for the model. First, we solved the model through HAM by choosing the preferred control parameter and also applied the RK4 method. The model solved by projected methods is compared with the NDSolver solution. The nature of the model is analyzed using different parameters, and the calculations are performed using Mathematica software. The obtained results are expressed in graphs and tables.
subject: Articles
  topic: section
subject: Homotopy analysis method
  topic: keywords
subject: Runge-Kutta method
  topic: keywords
subject: Caputo derivative
  topic: keywords
subject: Listeria infection model
  topic: keywords
subject: convergence
  topic: keywords
creator: Sachin K N
creator: Mallanagoud Mulimani
creator: Kumbinarasaiah S
creator: Suguntha Devi K
creator: Lavanya N
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-13
publication date: 2026-04-13
starting page: 520
ending page: 550
doi: 10.12150/jnma.2026.520

Numerical Solutions of Fuzzy Fractional Variable-Order Differential Equations
type: item
description: This paper addresses a class of fuzzy fractional differential equations (FFDEs) with variable-order (VO) derivatives, where the variable-order derivative is defined in the Caputo sense for fuzzy-valued functions. Using the $\Upsilon$-cut representation of fuzzy-valued functions, the original problem is reformulated into a new problem. To solve it, we apply operational matrices (OMs) derived from shifted Chebyshev polynomials of the third kind (SCP3). By approximating the unknown function and its derivative with SCP3, the problem is reduced to a system of nonlinear algebraic equations. A theoretical error analysis of the numerical solution is presented, along with an example to validate the method's accuracy.
subject: Articles
  topic: section
subject: Fuzzy fractional differential equations
  topic: keywords
subject: variable-order
  topic: keywords
subject: shifted Chebyshev polynomials of the third kind
  topic: keywords
subject: operational matrix
  topic: keywords
creator: Ghadah S. E. Noman
creator: D. D. Pawar
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-13
publication date: 2026-04-13
starting page: 494
ending page: 519
doi: 10.12150/jnma.2026.494

Stability Analysis of a Three-Dimensional Discrete Topp Model
type: item
description: Mathematical models of glucose, insulin, and pancreatic beta cell mass dynamics are essential for understanding the physiological basis of type 2 diabetes. This paper investigates the discrete-time dynamics of the Topp model to represent these interactions. We perform a comprehensive analysis of the system's trajectory, examining both local and global behavior. First, we establish the invariance of the positive trajectory and analyze the existence of fixed points. Then, we conduct a complete stability analysis, determining the local and global asymptotic stability of these fixed points. Finally, numerical examples validate the effectiveness and applicability of our theoretical findings. Additionally, we provide biological interpretations of our results.
subject: Articles
  topic: section
subject: Fixed point
  topic: keywords
subject: periodic point
  topic: keywords
subject: local stability
  topic: keywords
subject: global behavior
  topic: keywords
subject: regular operator
  topic: keywords
creator: Zafar Boxonov
creator: Utkir Rozikov
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-13
publication date: 2026-04-13
starting page: 474
ending page: 493
doi: 10.12150/jnma.2026.474

On Constacyclic Codes of Length $4p^s$ over $F_{p^m}[u,v]/\langle u^2, v^2, uv-vu \rangle$
type: item
description: In this paper, we determine the algebraic structure of all $\lambda$-constacyclic codes of length $4p^s$ over the ring $R_{u^2,v^2,p^m} = F_{p^m}[u,v]/\langle u^2, v^2, uv-vu \rangle$ and $u^2 = 0, v^2 = 0$ where $\lambda = (\alpha+\beta u+\gamma v+\delta uv)$ with $\beta,\gamma,\delta \in F_{p^m}$, $\alpha \in F_{p^m}^*$ and $\beta, \gamma$ are not both zero. If $\lambda$ is a square, each $\lambda$-constacyclic codes of length $4p^s$ is expressed as a direct sum of an -$\alpha$-constacyclic code and $\alpha$-constacyclic code of length $2p^s$. In the primary case where the unit $\lambda$ is not square, it is shown that any non-zero polynomial of degree $\leq 4$ over $F_{p^m}$ is invertible in the ring $R_{\alpha,\beta,\gamma,\delta} = R_{u^2,v^2,p^m}[x]/\langle x^{4p^s}-\lambda \rangle$ when $\lambda = (\alpha+\beta u+\gamma v +\delta uv)$ for non-zero elements $\alpha, \beta,\gamma \in F_{p^m}^*$, $\delta \in F_{p^m}$, it follows that the ring $R_{\alpha,\beta,\gamma,\delta}$ is a chain ring with maximal ideal $(x^4-\alpha_0)$ and $(\alpha+\beta u+\gamma v+\delta uv)$-constacyclic codes are $\langle (x^4-\alpha_0)^i \rangle$, for $0 \leq i \leq 2p^s$. In the second case where $\lambda$ is not square and $\lambda =\gamma$ for $\gamma \in F_{p^m}$, it is obtain that $R_{u^2,v^2,p^m}[x]/\langle x^{4p^s}-\gamma \rangle$ is a local ring with maximal ideal $\langle x^4-\gamma_0,u \rangle$ but not a chain ring, such $\lambda$-constacyclic codes are classified into four distinct types. We provide the number of codewords for each type, and give the details of their dual codes.
subject: Articles
  topic: section
subject: Constacyclic codes
  topic: keywords
subject: codes over rings
  topic: keywords
subject: dual codes
  topic: keywords
creator: Somaiyah A. A. Abdulsattar
creator: Arunkumar Patil
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-13
publication date: 2026-04-13
starting page: 453
ending page: 473
doi: 10.12150/jnma.2026.453

Solvability for a Class of Logarithmic Type Initial Conditions of Hadamard Fractional Differential System on an Infinite Interval
type: item
description: This paper investigates a class of Hadamard fractional differential system involving logarithmic type initial conditions on an infinite interval. Based on some obtained properties of the Green's functions, Schauder fixed point theorem and Banach contraction mapping principle, we establish the existence and uniqueness results for the system. Finally, we illustrate examples which show our main results.
subject: Articles
  topic: section
subject: Solvability
  topic: keywords
subject: Hadamard fractional differential system
  topic: keywords
subject: logarithmic type initial conditions
  topic: keywords
subject: infinite interval
  topic: keywords
creator: Chengbo Zhai
creator: Liting Bai
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-13
publication date: 2026-04-13
starting page: 431
ending page: 452
doi: 10.12150/jnma.2026.431

Dynamical Analysis of Virulence Evolution in Multistrain Infection Model Within Hosts
type: item
description: Understanding the evolutionary patterns of viral virulence characteristics from a microscopic perspective is crucial for effectively combating viral mutations. This paper investigates the dynamics of virulence trait development within healthy cells following pathogen invasion using adaptive dynamics, building on a viral dynamics model that accounts for multiple infectious strains within hosts. Ignoring viral evolution, stability analysis of equilibria reveals the competitive exclusion principle. When viral virulence evolves, we assume that the infection rate of healthy cells and the mortality rate of infected cells are functions of virulence. We establish global stability conditions for the system and examine the evolutionary trajectory of viral virulence using adaptive dynamics. Our results indicate that mutant viruses can cause trait substitution. The evolutionary singular strategy is identified as a continuously stable strategy without producing evolutionary branching. Furthermore, we consider the influence of certain parameters in the system on the evolution of singular strategies.
subject: Articles
  topic: section
subject: Viral infection model
  topic: keywords
subject: adaptive dynamics
  topic: keywords
subject: evolutionary singular strategy
  topic: keywords
subject: stability analysis
  topic: keywords
creator: Yayuan Lei
creator: Gang Huang
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-13
publication date: 2026-04-13
starting page: 405
ending page: 430
doi: 10.12150/jnma.2026.405

A Predator-Prey Biological Model of Multiple Species with Linear Growth Rates
type: item
description: The purpose of this paper is to give sufficient conditions for the existence and uniqueness of positive solutions to an elliptic system of the Dirichlet problem on a bounded domain $\Omega$ in $R^n$. Also considered are the effects of perturbations on the coexistence state and uniqueness. The techniques used in this paper are super-sub solutions method, eigenvalues of operators, maximum principles, spectrum estimates, inverse function theory, and general elliptic theory. The arguments also rely on some detailed properties for the solution of logistic equations. These results yield an algebraically computable criterion for the positive coexistence of species of animals with predator-prey relation in many biological models.
subject: Articles
  topic: section
subject: Predator-prey system
  topic: keywords
subject: coexistence state
  topic: keywords
subject: existence
  topic: keywords
subject: uniqueness
  topic: keywords
subject: perturbation
  topic: keywords
creator: Joon Hyuk Kang
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-13
publication date: 2026-04-13
starting page: 383
ending page: 404
doi: 10.12150/jnma.2026.383

Nonlinear Dynamics and Chaos in Fractional-Order Cardiac Action Potential Duration Mapping Model
type: item
description: This study introduces a novel one-dimensional fractional-order model for cardiac action potential duration (APD) dynamics, incorporating memory effects through discrete fractional calculus. By generalizing the classical APD map using the Caputo fractional difference operator, we uncover complex nonlinear behaviors not observed in traditional integer-order models. Through comprehensive numerical simulations, including bifurcation analysis and Lyapunov exponent calculations validated by the 0-1 test, we demonstrate that the fractional-order system exhibits: 1) Early onset of chaos (at $t_s = 307ms$) without preceding period-doubling bifurcations. 2) Novel rhythm alternations between 5 : 5 and 3 : 3 patterns. 3) Unique bistability phenomena, including 2 : 2 $\leftrightarrow$ chaos and 5 : 5 $\leftrightarrow$ 3 : 3 states. 4) Memory-dependent dynamics where current APD depends on all previous states. Our results reveal that fractional calculus provides a more physiologically realistic framework for modeling cardiac dynamics by naturally incorporating memory effects. The identified dynamical regimes offer new insights into the transition mechanisms from normal rhythms to potentially arrhythmic states, with particular clinical relevance to understanding alternans as precursors to ventricular fibrillation. The fractional-order approach demonstrates superior capability for capturing the complex, history-dependent nature of cardiac excitation compared with conventional models.
subject: Articles
  topic: section
subject: Fractional-order calculus
  topic: keywords
subject: cardiac dynamics
  topic: keywords
subject: action potential duration
  topic: keywords
subject: nonlinear dynamics
  topic: keywords
subject: chaos
  topic: keywords
creator: Rabah Bououden
creator: Tarek Houmor
creator: Fahd Jarad
creator: Mohammed S. Abdelouahab
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-13
publication date: 2026-04-13
starting page: 368
ending page: 382
doi: 10.12150/jnma.2026.368

A Semi-Analytical Study on SEIR Model with Vaccinated Effects
type: item
description: This research describes the dynamics of COVID-19 propagation using a mathematical model that considers vaccination and self-defence. Furthermore, the impact of vaccination on the development of disease transmission has been investigated. Our findings specifically show that putting into practice the best control measures, including time-dependent interventions, lowers the total infection load and disease transmission. Five different compartments (Susceptible, Exposed, Vaccinated, Infected, and Recovered) are used in this study to examine an epidemiological model of COVID-19 dynamics. Approximate analytical solutions to the model’s system of equations were obtained using the homotopy analysis method (HAM). The numerical simulation using MATLAB was employed to validate the accuracy and effectiveness of the solutions obtained through the Homotopy Analysis Method (HAM) by comparing the results. Excellent agreement is found when comparing the approximate analytical solution and the numerical simulation. The five-compartment model includes many more aspect parameters that are explored and graphically represented. These parameters include recovery rate and vaccination rate, among others. Moreover, it underscores the potential of the HAM as a powerful tool for exploring epidemic models and formulating control strategies.
subject: Articles
  topic: section
subject: Epidemic model
  topic: keywords
subject: COVID-19
  topic: keywords
subject: non-linear initial value problem
  topic: keywords
subject: Homotopy Analysis Method (HAM)
  topic: keywords
subject: numerical simulation
  topic: keywords
creator: V. Ananthaswamy
creator: B. Sathyapriya
creator: M. Shruthi
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-13
publication date: 2026-04-13
starting page: 338
ending page: 367
doi: 10.12150/jnma.2026.338

Geometric Inequality for CR-Slant Warped Product Submanifolds in Nearly Lorentzian Para-Sasakian Manifold
type: item
description: This paper examines CR-slant warped product submanifolds of the form $B \times_f N_\theta$ within a nearly Lorentzian para-Sasakian manifold. Here, $B$ represents a CR-product submanifold, $N_\theta$ is a slant submanifold and $f$ denotes the warping function. We establish an inequality relating the squared norm of the second fundamental form to the warping function, considering two cases based on the behavior of the structure vector field. Additionally, the conditions under which equality holds are investigated.
subject: Articles
  topic: section
subject: Warped product
  topic: keywords
subject: CR-slant submanifold
  topic: keywords
subject: nearly Lorentzian para-Sasakian manifold
  topic: keywords
creator: Lakshmi M S
creator: H. G. Nagaraja
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-13
publication date: 2026-04-13
starting page: 323
ending page: 337
doi: 10.12150/jnma.2026.323

Dynamical Analysis in a Discrete Fractional Order Harvested Predator-Prey Model Incorporating Fear Effect and Refuge
type: item
description: This paper examines the dynamics of a discrete fractional-order predator-prey model, incorporating the effects of fear, prey refuge, and population harvesting. The fractional-order framework, which accounts for memory-dependent processes, provides a more accurate depiction of biological interactions than traditional integer-order models. Fear is modeled as a factor that reduces predator-prey encounters, while prey refuge offers a sanctuary, altering population dynamics. The inclusion of harvesting further complicates prey population regulation. We identify the system’s equilibrium points and conduct a local stability analysis, focusing on the conditions that lead to stability, instability, and bifurcation. Specifically, we examine the Neimark-Sacker bifurcation, where a stable fixed point evolves into a closed periodic orbit. Numerical simulations corroborate the analytical findings, illustrating the pivotal roles that fear, refuge, and harvesting play in shaping system stability and long-term behavior.
subject: Articles
  topic: section
subject: Dynamical analysis
  topic: keywords
subject: predator-prey model
  topic: keywords
subject: harvesting
  topic: keywords
subject: fear effect
  topic: keywords
subject: refuge
  topic: keywords
subject: discrete fractional order
  topic: keywords
creator: Siti Nurul Afiyah
creator: Fatmawati
creator: Windarto
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-13
publication date: 2026-04-13
starting page: 305
ending page: 322
doi: 10.12150/jnma.2026.305

Modelling Zika Virus, Dengue Fever and Chikungunya Virus: Gaining Insights into the Co-Dynamics of the Three Diseases
type: item
description: The recent spike in the concurrent circulation of Zika, Dengue fever, and the Chikungunya virus poses a severe threat to public health, both at home and in the diaspora. This study dives into the interplay of these three diseases, applying mathematical analysis to explain their co-dynamics within a population where they coexist. A comprehensive investigation of the model indicates that the sub-models experience backward bifurcation when the relevant reproduction numbers for each disease fall below unity. To gain insights, real-life data from Espírito Santo State in Brazil, where both diseases are co-circulating and endemic, was gathered and incorporated into our model. This allowed us to estimate important parameter values that were embedded in the model. Through uncertainty and sensitivity analysis, we identified the top-ranked parameters that drive the spread of these three diseases, which are, effective contact rate of infected mosquitoes with susceptible humans, infected humans interacting with susceptible mosquitoes, and sexual transmission (specifically for the Zika virus). Simulations of the comprehensive Zika-Dengue-Chikungunya model revealed that minimizing the biting and contact rates of mosquitoes with humans decreases the disease load. Conversely, the absence of pesticide spraying and failure to utilize treated nets, together with unprotected sexual intercourse with sick individuals, result in the co-circulation of the three diseases, considerably aggravating the overall disease burden.
subject: Articles
  topic: section
subject: Modeling
  topic: keywords
subject: Zika virus
  topic: keywords
subject: Dengue fever
  topic: keywords
subject: Chikungunya
  topic: keywords
subject: co-infection
  topic: keywords
subject: stability analysis
  topic: keywords
creator: Nicholas Agahiu
creator: Benjamin Idoko Omede
creator: Olayemi Kehinde Samuel
creator: Abdullahi Ibrahim
creator: Bolarinwa Bolaji
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-04-13
publication date: 2026-04-13
starting page: 249
ending page: 304
doi: 10.12150/jnma.2026.249

ESS in a River Network with Two Branches
type: item
description: In a recent work by Jiang et al. [Bull. Math. Biol., 2020, Paper No. 131, 42pp], to discuss the impact of differing topology of river networks on the evolution of dispersal, the authors proposed three different models and found the winning of slower/faster diffuser or evolutionarily singular strategies. However, it is unknown whether there is an evolutionarily stable strategy (ESS, a central concept in evolution game theory) for these three models. In this paper, focusing on the Model (III) proposed by them (the most complicated one as they stated), we give a confirmed answer to this issue, that is, there does exist ESS.
subject: Articles
  topic: section
subject: Evolution of dispersal
  topic: keywords
subject: evolutionarily stable strategy
  topic: keywords
subject: advective patchy environment
  topic: keywords
subject: selection gradient
  topic: keywords
creator: Gongyi Jin
creator: Xiaoqian Feng
creator: Peng Zhou
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-01-23
publication date: 2026-01-23
starting page: 229
ending page: 248
doi: 10.12150/jnma.2026.229

Cross-Invariant Sets of the Cubic Nonlinear Schrödinger System with Partial Confinement
type: item
description: This paper studies the cubic nonlinear Schrödinger system with partial confinement: \begin{cases}-i\varphi_t + (x_1^2 + x_2^2)\varphi = \Delta\varphi +\mu_1|\varphi|^2\varphi + \beta|\psi|^2\varphi, & (t,x) \in \mathbb{R}^+\times \mathbb{R}^3, \\ -i\psi_t + (x_1^2 + x_2^2)\psi =\Delta\psi + \mu_2|\psi|^2\psi + \beta|\varphi|^2\psi, & (t,x) \in\mathbb{R}^+ \times \mathbb{R}^3,\end{cases} which models the Bose-Einstein condensates with multiple states or the propagation of mutually incoherent wave packets in nonlinear optics. The cross-invariant sets of the evolution flow are obtained by constructing the cross-constrained variational problem. Furthermore, the sharp condition for global existence and blowup of the solutions is derived.
subject: Articles
  topic: section
subject: Bose-Einstein condensates
  topic: keywords
subject: nonlinear Schrödinger system
  topic: keywords
subject: cross-invariant sets
  topic: keywords
subject: sharp condition
  topic: keywords
subject: global existence
  topic: keywords
creator: Xinlu Zhou
creator: Jian Zhang
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-01-23
publication date: 2026-01-23
starting page: 217
ending page: 228
doi: 10.12150/jnma.2026.217

Analysis of a Fractional Order Eco-Epidemiological Model with Prey Infection and Predator Cannibalism
type: item
description: This study proposes a fractional-order prey-predator model that integrates disease dynamics within prey populations, fear induced behavioral responses, and predator cannibalism. The prey population is divided into susceptible and infected classes to represent disease dynamics effectively, while predator cannibalism is modeled as a survival strategy during prey scarcity. Essential properties such as non-negativity, boundedness, and the existence and uniqueness of solutions are thoroughly examined. Stability of equilibrium points is established, and global stability is proved using Lyapunov functions. Numerical simulations validate the theoretical results, highlighting how variations in cannibalism rates and fractional-order parameters influence population dynamics and system behavior.
subject: Articles
  topic: section
subject: Predator-prey system
  topic: keywords
subject: Caputo fractional-order derivative
  topic: keywords
subject: eco-epidemiological model
  topic: keywords
subject: cannibalism
  topic: keywords
subject: stability
  topic: keywords
creator: S. Karthikeyan
creator: M. Sambath
creator: K. Balachandran
creator: M. S. Muthuvalu
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-01-23
publication date: 2026-01-23
starting page: 198
ending page: 216
doi: 10.12150/jnma.2026.198

Optimal Control Approach for Bilateral Elastic Contact Problem with Power-Law Friction
type: item
description: We use the control variational technique to examine an elastic contact model, subject to a non-penetration condition in the normal direction and to power-law friction, proving the unique existence of the solution. This method uses optimal control theory to minimize the energy functional of the nonlinear equation. A multivalued equation $f\in \mathcal{F}y+∂\Phi(y)$ for the displacement field describes the problem in a weak formulation, where a linear mapping is represented by $\mathcal{F},$ and the Clarke’s subdifferential of the mapping $\Phi$ is indicated by $∂\Phi.$ We employ abstract existence theorems to verify the unique weak solution to the contact model.
subject: Articles
  topic: section
subject: Optimal control approach
  topic: keywords
subject: multivalued equation
  topic: keywords
subject: Clarke subdifferential
  topic: keywords
subject: elastic materials
  topic: keywords
subject: bilateral contact problem
  topic: keywords
subject: normal compliance condition
  topic: keywords
subject: Coulomb dry friction (power-law friction)
  topic: keywords
creator: O. Atelaue
creator: Z. Faiz
creator: R. Bouchantouf
creator: H. Benaissa
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-01-23
publication date: 2026-01-23
starting page: 185
ending page: 197
doi: 10.12150/jnma.2026.185

Nonlinear Dynamics and Pull-in Phenomena in a Magneto-Electro MEMS Actuator with Hardening Spring
type: item
description: This paper investigates the dynamic behavior and pull-in instability of a magneto-electro Micro-Electro-Mechanical System (MEMS) actuator, focusing on the nonlinear effects arising from magnetic forces and spring stiffness. The system consists of a movable wire attracted toward a stationary wire due to magnetic forces generated by applied currents. A critical equilibrium, known as the pull-in point, is reached when the currents exceed a threshold, leading to instability. We consider the governing equation based on Newton’s Second Law, incorporating a nonlinear restoring force for the spring, which exhibits hardening behavior. The resulting second-order differential equation is analyzed using qualitative and bifurcation theories, revealing the critical bifurcation values determined by the currents and spring stiffness. Through a dynamical systems approach, we characterize the phase portraits and solutions, identifying distinct dynamical behaviors and the conditions for pull-in instability. Numerical simulations are performed to validate the analytical predictions, demonstrating excellent agreement with the theoretically derived threshold.
subject: Articles
  topic: section
subject: MEMS
  topic: keywords
subject: magneto-electro actuator
  topic: keywords
subject: nonlinear hardening spring
  topic: keywords
subject: pull-in instability
  topic: keywords
subject: bifurcation and qualitative analysis
  topic: keywords
creator: Lijun Zhang
creator: Jun Ma
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-01-23
publication date: 2026-01-23
starting page: 170
ending page: 184
doi: 10.12150/jnma.2026.170

On the Numerical Solution of Solidification of Water
type: item
description: The objective of this paper is to find an economical computer algorithm using a third-degree polynomial for the free boundary problem corresponding to phase change problem. We solve the problem to obtain the approximate analytical expression for the temperature distribution and the movement of the interface using the constrained integral method. Results are validated against existing numerical methods, demonstrating strong agreement with other techniques.
subject: Articles
  topic: section
subject: Constrained integral method
  topic: keywords
subject: melting and solidification
  topic: keywords
subject: moving boundary problem
  topic: keywords
subject: Stefan problem
  topic: keywords
subject: phase change
  topic: keywords
subject: ice bank
  topic: keywords
creator: Abdellatif Boureghda
creator: Soumaya Belabbes
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-01-23
publication date: 2026-01-23
starting page: 160
ending page: 169
doi: 10.12150/jnma.2026.160

Generalized Variational Inclusion Problem Involving Averaged Operator and Cayley Operator
type: item
description: In this paper, we consider and study a variational inclusion problem involving averaged and Cayley operators in the context of a Hilbert space. It is shown that our problem is equivalent to a fixed-point equation. We define an iterative algorithm based on a fixed-point formulation to obtain the solution. Our result is supported by a numerical example, computation tables, and a convergence graph are also provided.
subject: Articles
  topic: section
subject: Cayley operator
  topic: keywords
subject: averaged operator
  topic: keywords
subject: variational inclusion
  topic: keywords
subject: resolved operator
  topic: keywords
creator: Mohd. Falahat Khan
creator: Syed Shakaib Irfan
creator: Rais Ahmad
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-01-23
publication date: 2026-01-23
starting page: 145
ending page: 159
doi: 10.12150/jnma.2026.145

Stability Analysis of a Diffusive Ratio-Dependent Predator-Prey Model with Nonlocal Perception
type: item
description: In this paper, we propose a diffusive ratio-dependent predator-prey model with a nonlocal perceptual term. We first discuss the well-posedness of solutions. Then for the model without the nonlocal perception term, we obtain stability conditions of the spatially homogeneous steady state. Under these conditions, when considering the effects of nonlocal perception, our result indicates that if the system without nonlocal perception term is stable, and even after introducing nonlocal perception term, the system remains stable. However, if the system without nonlocal perception term is unstable, and the introduction of nonlocal perception term will make the system become stable.
subject: Articles
  topic: section
subject: Predator-prey model
  topic: keywords
subject: nonlocal perception
  topic: keywords
subject: stability
  topic: keywords
creator: Lu Zheng
creator: Yahong Peng
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-01-23
publication date: 2026-01-23
starting page: 131
ending page: 144
doi: 10.12150/jnma.2026.131

The Impact of Educational Campaigns on the Global Dynamics of Cholera Epidemics
type: item
description: In this study, we examine a cholera epidemic model that incorporates educational transmission and delve into the long-term dynamics of the epidemic equilibrium point, particularly in relation to the spread of information about disease transmission. We find that if the basic reproduction number $R_0$ is less than or equal to 1, the disease is destined to be eradicated, and the unique disease-free equilibrium point becomes globally stable. It is noteworthy that the stability of this disease-free equilibrium is not influenced by the extent of disease education, the variety of infections, or the rate of education. On the other hand, if the basic reproduction number is greater than 1, we study the existence of the endemic equilibrium, and demonstrate that the disease will persist if $β_0$ > $D_0$. To assess the impact of educational campaigns on disease control, we further establish the asymptotic behavior of both infected and susceptible populations in response to educational interventions. Our findings indicate that well-executed educational campaigns can substantially contribute to the management and mitigation of the disease’s effects.
subject: Articles
  topic: section
subject: Cholera epidemic model
  topic: keywords
subject: education communication
  topic: keywords
subject: asymptotic behavior
  topic: keywords
creator: Zexin Sun
creator: Xiongxiong Bao
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-01-23
publication date: 2026-01-23
starting page: 110
ending page: 130
doi: 10.12150/jnma.2026.110

Existence Results for a Generalized $p$($x$)-Biharmonic Problem Type with No-Flux Boundary Condition
type: item
description: This paper aims to study the existence and multiplicity of weak solutions for a problem involving a generalized $p$($x$)-biharmonic operator with no flux boundary condition. By using the variational techniques and the theory of the variable exponent Lebesgue spaces, we obtain the existence of at least one nontrivial solution and at least $n$ distinct pairs of nontrivial weak solutions to this problem, respectively.
subject: Articles
  topic: section
subject: No-flux boundary condition
  topic: keywords
subject: $p$($x$)-biharmonic problem type
  topic: keywords
subject: variational methods
  topic: keywords
creator: Youssef Zine.eddine
creator: Mohamed Talbi
creator: Najib Tsouli
creator: Mohammed Filali
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-01-23
publication date: 2026-01-23
starting page: 94
ending page: 109
doi: 10.12150/jnma.2026.94

MEK Inhibition May Prevent the Recruitment of NK Cells in the Tumor Microenvironment: A Mathematical Model of Glioma Treatment
type: item
description: In this paper, we analyze the dynamics of oncolytic virotherapy combined with MEK inhibitors for the treatment of glioma. Although the therapeutic effect of oncolytic viruses (OV) depends on the recruitment of NK cells, these viruses are frequently subject to NK cell clearance, which may reduce the efficacy of oncolytic virotherapy. Furthermore, it is more challenging for OV to enter glioma cells because these cells lack Coxsackievirus and Adenovirus Receptors (CAR). MEK inhibitors, however, are able to compensate for this deficiency in CAR molecules. Herein, we propose and analyze a mathematical model of the dynamics of cancer cells, oncolytic viruses, activated NK cells, and CAR molecules while combining oncolytic virotherapy with MEK inhibition. Our goal is to identify the circumstances in which the treatment may be effective. In this research, we investigated the existence of equilibrium points. The two endemic equilibriums and the virus infection-free equilibrium stability conditions are given. The findings demonstrate that, in a dynamical system, NK cell activation can either establish or destroy equilibrium points and that substantial recruitment of activated NK cells might have detrimental effects on oncolytic virotherapy. However, MEK inhibitors boost OV effectiveness and may prevent NK cell recruitment.
subject: Articles
  topic: section
subject: Glioma
  topic: keywords
subject: cancer
  topic: keywords
subject: oncolytic virotherapy
  topic: keywords
subject: MEK inhibitors
  topic: keywords
subject: mathematical model
  topic: keywords
creator: Amine Alabkari
creator: Ahmed Kourrad
creator: Khalid Adnaoui
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-01-23
publication date: 2026-01-23
starting page: 72
ending page: 93
doi: 10.12150/jnma.2026.72

Local Ground-State and Mountain Pass Solutions for a $p$-Kirchhoff Equation with Critical Exponent
type: item
description: We study a Kirchhoff-type equation where the diffusion coefficient is non-locally affected, the nonlinear diffusion phenomenon is governed by the $p$-Laplace operator and the population supply presents critical growth. The energy functional associated with the equation is not bounded from below so that there is no global ground-state; however, we prove the existence of a positive local ground-state. We also prove that the equation has a positive solution of mountain pass type. The concentration-compactness principle is a main tool in our approach.
subject: Articles
  topic: section
subject: Integro-differential equation
  topic: keywords
subject: $p$-Kirchhoff equation
  topic: keywords
subject: critical exponent
  topic: keywords
subject: mountain-pass solution
  topic: keywords
subject: local ground-state solution
  topic: keywords
creator: Juan Mayorga-Zambrano
creator: Henry Cumbal-López
creator: Daniel Narváez-Vaca
creator: Jordy Cevallos-Chávez
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-01-23
publication date: 2026-01-23
starting page: 52
ending page: 71
doi: 10.12150/jnma.2026.52

A Mathematical Modeling of Two-Strain Tuberculosis Transmission: Deterministic and Stochastic Approaches to Screening, Treatment, and Quarantine Strategies
type: item
description: This research observes the transmission dynamics of drug-sensitive tuberculosis (DS-TB), drug-resistant tuberculosis (DR-TB) and undiagnosed tuberculosis infections using deterministic and stochastic models. The study focuses on the impacts of contact rates, screening of latent individuals or high-risk groups, treatment, and quarantine measures on the basic reproduction rate ($R_0$) and the estimated number of infected individuals ($m$). The results show that undiagnosed infected individuals are the greatest factor on the spread of tuberculosis within the system, which emphasizes the importance of screening on latent individuals. Analysis on the effects of screening on latent individuals also emphasizes the importance of treatment and quarantine for both DS-TB and DR-TB infections, respectively. However, analysis on the effects of both treatment and quarantine states that relying on either treatment or quarantine efforts is not enough to stop the spread of the two-strain TB within the system; thus a combined strategies is required to help eradicate the disease.
subject: Articles
  topic: section
subject: Deterministic model
  topic: keywords
subject: stochastic model
  topic: keywords
subject: screening
  topic: keywords
subject: treatment
  topic: keywords
subject: quarantine
  topic: keywords
creator: A. Muhammad Mu’adz
creator: Kasbawati
creator: Syamsuddin Toaha
creator: Muhammad Rifqy Adha Nurdiansyah
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-01-23
publication date: 2026-01-23
starting page: 30
ending page: 51
doi: 10.12150/jnma.2026.30