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: 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
items: Bullen-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings with Applications
items: New Refinements of Hermite-Hadamard Inequalities for Quantum Integrals
items: The Second-Order Melnikov Function and Chaotic Tangles on Toral van der Pol Equation
items: Application of the Functional Variable Method to Some Nonlinear Evolution Equations
items: Bifurcation Analysis of Predator-Prey Mathematical Model with Resource-Limited Growth and Predator Switching Behavior
items: A Semi-Analytical Study of a Non-Linear Initial Value Problem for the Lassa Fever Model
items: Fractional Order Solution to Analyze Tumor-Immune Cells by Using Hybrid Natural Transform Method and Residual Power Series Method
items: Properties Around the First Eigenvalue of a Partial Discrete Dirichlet Boundary Value Problem
items: Exact Soliton of Fifth Order (1+1) Dimensional Triple Non-Linear Partial Differential Equations on Modified Truncated Expansion Methods
items: Dynamical Properties of a Stochastic Tumor-Immune Model with Pulsed Chemotherapeutic Dose Response
items: Three Solutions for a Perturbed Integral Equation with Homogeneous Dirichlet Condition
items: On Dynamics of Certain Models via Generalized Conformable Fractional Derivative
items: Minimizing the Eigenvalue Ratio for the $p$-Laplacian Operator
items: A New Study on Common Fixed Points for ($α$-$β$-$F$)-Contraction Mappings
items: Bifurcation Analysis of a Discrete Predator-Prey Model with Gompertz Growth and Increased Functional Response
items: Spatiotemporal Dynamics of a Memory-Diffusion Predator-Prey System with Two Delays and Nonlocal Competition
items: A New Approach to Hermite-Hadamard-Type Inequality with Proportional Caputo-Hybrid Operator

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

Bullen-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings with Applications
type: item
description: In this paper, we first introduce a novel extension of the Bullen-type inequalities using Riemann-Liouville integral operators and establish a generalized fractional integral identity of the Bullen type. Next, we derive integral inequalities related to the Bullen-type inequalities for twice-differentiable mappings, utilizing this novel extended identity. To demonstrate these inequalities, we provide examples along with corresponding graphs. Furthermore, we investigate how these inequalities can be practically applied to mean inequalities, contributing to a deeper comprehension and wider usefulness of these mathematical ideas. Finally, the inequalities given in this work extend several known inequalities in the literature, which is the main advantage of the newly found inequalities.
subject: Articles
  topic: section
subject: Bullen-type inequalities
  topic: keywords
subject: Hermite-Hadamard-type inequalities
  topic: keywords
subject: convex functions
  topic: keywords
subject: Riemann-Liouville fractional integrals
  topic: keywords
subject: special means
  topic: keywords
creator: Mehmet Zeki Sarıkaya
creator: Tuba Tunç
creator: İzzettin Demir
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-01-23
publication date: 2026-01-23
starting page: 9
ending page: 29
doi: 10.12150/jnma.2026.9

New Refinements of Hermite-Hadamard Inequalities for Quantum Integrals
type: item
description: In this study, we first introduce two functions including quantum integrals. Then, we prove some properties of these mappings such as convexity and monotony. Moreover, by using the newly defined mappings, we prove some refinements of the left hand side of Hermite-Hadamard inequality for left and right quantum integrals.
subject: Articles
  topic: section
subject: Convex functions
  topic: keywords
subject: Hermite-Hadamard inequality
  topic: keywords
subject: quantum integrals
  topic: keywords
creator: Hüseyin Budak
rights: Copyright (c) 2026 Journal of Nonlinear Modeling and Analysis
date: 2026-01-23
publication date: 2026-01-23
starting page: 1
ending page: 8
doi: 10.12150/jnma.2026.1

The Second-Order Melnikov Function and Chaotic Tangles on Toral van der Pol Equation
type: item
description: The van der Pol equation on the torus is considered. This equation contains a heteroclinic cycle consisting of four symmetric heteroclinic orbits. By high order Melnikov method, the periodic forced van der Pol equation is investigated and chaotic dynamics is obtained. An explicit formula of the second-order Melnikov function is derived for the splitting heteroclinic connection. It is used to detect chaotic dynamics when the first-order(classical) Melnikov function is degenerate. By the second-order Melnikov function, we deduce chaotic heteroclinic tangles with rigorously theoretical analysis as well as numerical simulations.
subject: Articles
  topic: section
subject: Van der Pol equation
  topic: keywords
subject: high order Melnikov method
  topic: keywords
subject: heteroclinic tangles
  topic: keywords
creator: Fengjuan Chen
creator: Mei Chen
creator: Yi Zhong
rights: Copyright (c) 2025 Journal of Nonlinear Modeling and Analysis
date: 2025-11-26
publication date: 2025-11-26
starting page: 2001
ending page: 2012
doi: 10.12150/jnma.2025.2001

Application of the Functional Variable Method to Some Nonlinear Evolution Equations
type: item
description: The functional variable method is a highly effective approach for deriving exact solutions to nonlinear evolution equations. It offers broad applicability in addressing nonlinear wave equations. In this paper, the functional variable method is employed to obtain soliton solutions for the Radhakrishnan-Kundu-Lakshmanan (RKL) equation and the Landau-Ginzburg-Higgs equation. Exact solutions play a crucial role in uncovering the internal mechanisms of physical phenomena. Graphical representations of the obtained optical soliton solutions are provided to illustrate some of their physical parameters.
subject: Articles
  topic: section
subject: Solitary wave solution
  topic: keywords
subject: Radhakrishnan-Kundu-Lakshmanan equation
  topic: keywords
subject: Landau-Ginzburg-Higgs equation
  topic: keywords
subject: functional variable method
  topic: keywords
creator: Patanjali Sharma
rights: Copyright (c) 2025 Journal of Nonlinear Modeling and Analysis
date: 2025-11-26
publication date: 2025-11-26
starting page: 2379
ending page: 2391
doi: 10.12150/jnma.2025.2379

Bifurcation Analysis of Predator-Prey Mathematical Model with Resource-Limited Growth and Predator Switching Behavior
type: item
description: Ecology examines the interactions between organisms and their environment, with a particular focus on population dynamics, resource availability, and predator-prey relationships. This study presents a mathematical model designed to investigate the interactions between two prey populations, one in an unprotected region and the other in a protected region, along with a predator population and shared resource availability. The model employs nonlinear differential equations to capture processes such as prey growth, predation, and resource utilization. By identifying equilibrium points and conducting eigenvalue analysis, we assess the system’s stability. Numerical simulations demonstrate a range of outcomes, including stable states, cyclic behavior, and population collapse, depending on ecological conditions (parametric values). Biologically, predator-prey coexistence equilibria may lose stability, shifting to extinction or dominance scenarios. This makes bifurcation point. Bifurcation analysis reveals how competition and predation impact stability, with critical points marking transitions between coexistence, oscillations, or extinction. These results underscore the intricate balance of ecological forces and emphasize the significance of resource management and conservation in preserving ecosystem stability.
subject: Articles
  topic: section
subject: Ecology
  topic: keywords
subject: predator-prey model
  topic: keywords
subject: resource availability
  topic: keywords
subject: stability analysis
  topic: keywords
subject: local bifurcation
  topic: keywords
creator: Negeri Negese Wayesa
creator: Legesa Lemecha Obsu
creator: Mohammed Yiha Dawed
rights: Copyright (c) 2025 Journal of Nonlinear Modeling and Analysis
date: 2025-11-26
publication date: 2025-11-26
starting page: 2349
ending page: 2378
doi: 10.12150/jnma.2025.2349

A Semi-Analytical Study of a Non-Linear Initial Value Problem for the Lassa Fever Model
type: item
description: Mathematical modelling plays a crucial role in comprehending and exercising control over Lassa fever outbreaks. The Homotopy Analysis Method (HAM) is employed to address the system of nonlinear differential equations and generate a semi-analytical solution for the Lassa disease Susceptible-Exposed-Infected-Recovered (SEIR) model. Comparing with numerical simulations, the HAM technique yielded extremely precise approximate solutions, proving its accuracy and efficiency. The numerical simulation is carried out using MATLAB programming. There is a good agreement between the numerical simulation and the approximate analytical results. We also examine the effects of changing model parameters on the different compartments, obtaining insightful knowledge on how the model behaves in various scenarios. This analysis is crucial for understanding how variations in transmission rates, recovery rates, and other key factors affect the overall dynamics of Lassa fever, thereby guiding more effective public health strategies and disease management. Moreover, it underscores the potential of the Homotopy Analysis Method (HAM) as a powerful tool for exploring epidemic models and formulating control strategies.
subject: Articles
  topic: section
subject: Epidemic model
  topic: keywords
subject: Lassa fever
  topic: keywords
subject: non-linear initial value problem
  topic: keywords
subject: homotopy analysis method (HAM)
  topic: keywords
subject: numerical simulation
  topic: keywords
creator: S. Meenakshi
creator: V. Ananthaswamy
creator: M. Shruthi
rights: Copyright (c) 2025 Journal of Nonlinear Modeling and Analysis
date: 2025-11-26
publication date: 2025-11-26
starting page: 2330
ending page: 2348
doi: 10.12150/jnma.2025.2330

Fractional Order Solution to Analyze Tumor-Immune Cells by Using Hybrid Natural Transform Method and Residual Power Series Method
type: item
description: The purpose of this study is to examine the impact of fractional-order chemotherapy drug diffusion on tumor-immune cell growth. To address the proposed system of fractional-order tumor-immune cell dynamics, two distinct and robust methods have been employed. Initially, the Hybrid Natural Decomposition method, an analytical approach that merges two effective techniques – Natural Transform and the Adomian Decomposition Method has been applied. Subsequently, the Residual Power Series method, a numerical technique, has been employed to derive the solution in series form. The graphical comparison of the results obtained from both methods with those from classical-order solutions has been provided. The findings clearly demonstrate that the proposed approaches offer a reliable and accurate means of understanding the intricate interactions between tumor growth and immune cell activity.
subject: Articles
  topic: section
subject: Chemotherapy
  topic: keywords
subject: cancer
  topic: keywords
subject: Residual Power Series method
  topic: keywords
subject: Natural Transform method
  topic: keywords
subject: tumor immune cell
  topic: keywords
subject: fractional derivative
  topic: keywords
subject: Adomian polynomials
  topic: keywords
creator: Ashrita Patra
creator: Tapasi Pasayat
rights: Copyright (c) 2025 Journal of Nonlinear Modeling and Analysis
date: 2025-11-26
publication date: 2025-11-26
starting page: 2314
ending page: 2329
doi: 10.12150/jnma.2025.2314

Properties Around the First Eigenvalue of a Partial Discrete Dirichlet Boundary Value Problem
type: item
description: In this article, we study some results around the first eigenvalue $\lambda_{1,m}$ for the partial discrete Dirichlet boundary value problem, like the constant sign of the eigenfunction associated with $\lambda_{1,m}$, the simplicity of $\lambda_{1,m}$ and the sign change of any eigenfunction associated with $\lambda > \lambda_{1,m}$.
subject: Articles
  topic: section
subject: Partial discrete Dirichlet problem
  topic: keywords
subject: first eigenvalue
  topic: keywords
subject: simplicity
  topic: keywords
creator: Mohammed Abderrahim
creator: Abdesslem Ayoujil
creator: Mohammed Barghouthe
creator: Mohammed Berrajaa
rights: Copyright (c) 2025 Journal of Nonlinear Modeling and Analysis
date: 2025-11-26
publication date: 2025-11-26
starting page: 2300
ending page: 2313
doi: 10.12150/jnma.2025.2300

Exact Soliton of Fifth Order (1+1) Dimensional Triple Non-Linear Partial Differential Equations on Modified Truncated Expansion Methods
type: item
description: In this manuscript, modified truncated expansion method-I taking the traveling wave variable $u(x, t)=y(r)=y(kx+wt)$ and modified truncated expansion method-II introducing the traveling wave variable $u(x, t) = y(r)=y(kx − wt)$ are built up to obtain analytical solution in the form of traveling wave solutions with different frequencies and velocities that can be constructed for triple (1+1) dimensional nonlinear partial differential equations (NLPDEs) such as Sawada-Kotera equation (SKE), generalized Korteweg-de Vries equation (GKdVE) and Kaup-Kuperschmidt equation (KKE), which have been widely used in mathematical physics. The present topic minimizes the complex nature and non-integrable characteristics to obtain solutions of NLPDEs. To demonstrate the influence of the parameters, 3D plots are generated for triple NLPDEs. This content is employed in physics such as magneto sound in plasma and nonlinear optics.
subject: Articles
  topic: section
subject: Modified truncated expansion methods
  topic: keywords
subject: triple nonlinear partial differential equations
  topic: keywords
subject: magneto sound in plasma
  topic: keywords
subject: nonlinear optics
  topic: keywords
subject: traveling wave solutions
  topic: keywords
creator: Satyajit Mohapatra
creator: Saumya Ranjan Jena
rights: Copyright (c) 2025 Journal of Nonlinear Modeling and Analysis
date: 2025-11-26
publication date: 2025-11-26
starting page: 2285
ending page: 2299
doi: 10.12150/jnma.2025.2285

Dynamical Properties of a Stochastic Tumor-Immune Model with Pulsed Chemotherapeutic Dose Response
type: item
description: Comprehensive pulsed chemotherapy and immunotherapy are widely employed in clinical tumor treatment. Given the periodically pulsed nature of this approach, we propose a stochastic tumor-immune dynamical model with a pulsed chemotherapeutic dose response. The model accounts for the combined effects of pulsed chemotherapy and pulsed immunotherapy, as well as the influence of environmental random disturbances. We prove the existence and uniqueness of a global positive solution to the proposed model. By using comparison theorems for impulsive differential equations, we show the boundedness of the solution’s expectation. Furthermore, we derive sufficient conditions for the extinction and non-persistence in the mean of tumor cells, hunting T-cells, and helper T-cells, as well as for the weak persistence in the mean of tumor cells and helper T-cells, and the stochastic persistence of tumor cells. The results of our study, supported by numerical simulations, demonstrate that random disturbances can effectively inhibit tumor cell growth.
subject: Articles
  topic: section
subject: Tumor-immune model
  topic: keywords
subject: chemotherapeutic dose response
  topic: keywords
subject: random disturbances
  topic: keywords
subject: Itô’s formula
  topic: keywords
subject: impulsive stochastic differential equation
  topic: keywords
creator: N. Bajja
creator: D. Seghir
rights: Copyright (c) 2025 Journal of Nonlinear Modeling and Analysis
date: 2025-11-26
publication date: 2025-11-26
starting page: 2261
ending page: 2284
doi: 10.12150/jnma.2025.2261

Three Solutions for a Perturbed Integral Equation with Homogeneous Dirichlet Condition
type: item
description: We consider the integral equation $-\mathcal{L}_K^p u = \lambda f(x,u) + \mu g(x,u),$ with homogeneous Dirichlet condition on a bounded Lipschitz domain of $\mathbb{R}^N$ where $\lambda, \mu \in \mathbb{R},$ $p \geq 2,$ $s \in ]0,1[,$ $N > ps,$ $f,g : \mathbb{R}^N \rightarrow \mathbb{R}$ are Carathéodory functions with subcritical growth and $-\mathcal{L}^p$ denotes a class of operators that includes $(-\Delta)_p^s,$ the fractional $p$-Laplacian. Here $\mu g$ represents a small perturbation of $\lambda f.$ Applying an abstract critical point theorem due to Ricceri, a variational setting developed by Xiang et al. and a Minti-Browder's theorem, we prove the existence of three weak solutions.
subject: Articles
  topic: section
subject: Integral elliptic equation
  topic: keywords
subject: variational methods
  topic: keywords
subject: critical points
  topic: keywords
creator: Andre Vera-Montiel
creator: Juan Mayorga-Zambrano
rights: Copyright (c) 2025 Journal of Nonlinear Modeling and Analysis
date: 2025-11-26
publication date: 2025-11-26
starting page: 2247
ending page: 2260
doi: 10.12150/jnma.2025.2247

On Dynamics of Certain Models via Generalized Conformable Fractional Derivative
type: item
description: This paper deals with the generalized conformable fractional derivative and certain interesting properties which are not compatible with Riemann-Liouville and Caputo fractional derivatives. The newly defined derivative is more efficient than other conformable fractional derivatives and the nonlocal fractional derivatives from a time perspective. To justify the claim, we provide some direct applications, such as population growth, Newton’s body cooling, heat equation and susceptible-infected-removed models. Solutions obtained from models and comparison with respective previous data are demonstrated with the help of graphs or stems.
subject: Articles
  topic: section
subject: Fractional derivative
  topic: keywords
subject: SECH-fractional derivative
  topic: keywords
subject: fractional population growth model
  topic: keywords
subject: fractional body cooling model
  topic: keywords
subject: fractional heat equation
  topic: keywords
subject: SIR model
  topic: keywords
creator: Pinakadhar Baliarsingh
creator: Swaraj Sahoo
rights: Copyright (c) 2025 Journal of Nonlinear Modeling and Analysis
date: 2025-11-26
publication date: 2025-11-26
starting page: 2224
ending page: 2246
doi: 10.12150/jnma.2025.2224

Minimizing the Eigenvalue Ratio for the $p$-Laplacian Operator
type: item
description: We focus on the minimization problem of the eigenvalue ratio for the $p$-Laplacian operator with Robin boundary conditions on an interval $[0, \hat{π}],$ where $\hat{\pi} = \frac{2\pi}{p \sin(\pi/p)}.$ Using variational techniques and Prüfer-type transformations, we show that the constant weight is not minimizing for the class of concave weights.
subject: Articles
  topic: section
subject: Eigenvalue ratio
  topic: keywords
subject: $p$-Laplacian operator
  topic: keywords
subject: concave weight
  topic: keywords
subject: Robin boundary conditions
  topic: keywords
creator: Mohammed Ahrami
creator: Zakaria El Allali
creator: Jamal Ounejma
rights: Copyright (c) 2025 Journal of Nonlinear Modeling and Analysis
date: 2025-11-26
publication date: 2025-11-26
starting page: 2213
ending page: 2223
doi: 10.12150/jnma.2025.2213

A New Study on Common Fixed Points for ($α$-$β$-$F$)-Contraction Mappings
type: item
description: This paper explores the existence of common fixed points for a newly introduced class of mappings called ($α$-$β$-$F$)-contraction mappings in metric spaces. We establish several common fixed point theorems under specific conditions, incorporating ($α$-$β$-$F$)-weak contractions to extend and generalize existing results in fixed point theory. Unlike many classical approaches, our framework retains flexibility while accommodating key structural properties such as compactness and continuity. To support the theoretical findings, illustrative examples are provided. These results enhance the understanding and applicability of fixed point theory.
subject: Articles
  topic: section
subject: Common fixed point
  topic: keywords
subject: ($α$-$β$-$F$)-contraction
  topic: keywords
subject: ($α$-$β$-$F$)-weak contraction
  topic: keywords
creator: Saeed A. A. Al-Salehi
creator: Mohammed M. A. Taleb
creator: V. C. Borkar
rights: Copyright (c) 2025 Journal of Nonlinear Modeling and Analysis
date: 2025-11-26
publication date: 2025-11-26
starting page: 2201
ending page: 2212
doi: 10.12150/jnma.2025.2201

Bifurcation Analysis of a Discrete Predator-Prey Model with Gompertz Growth and Increased Functional Response
type: item
description: This study examines a discrete predator-prey model that employs a Gompertz growth function for the prey and a Holling type I functional response. Initially, the research explores the existence and local stability of fixed points within the system, employing a fundamental lemma. Subsequently, the conditions necessary for the emergence of transcritical and Neimark-Sacker bifurcations of the system are established through the application of the center manifold theorem and bifurcation theory. Finally, numerical simulations are performed to confirm the existence of the Neimark-Sacker bifurcation.
subject: Articles
  topic: section
subject: Discrete predator-prey system
  topic: keywords
subject: semidiscretization method
  topic: keywords
subject: Gompertz growth model
  topic: keywords
subject: transcritical bifurcation
  topic: keywords
subject: Neimark-Sacker bifurcation
  topic: keywords
creator: Xianyi Li
creator: Jun Xie
rights: Copyright (c) 2025 Journal of Nonlinear Modeling and Analysis
date: 2025-11-26
publication date: 2025-11-26
starting page: 2182
ending page: 2200
doi: 10.12150/jnma.2025.2182

Spatiotemporal Dynamics of a Memory-Diffusion Predator-Prey System with Two Delays and Nonlocal Competition
type: item
description: Predator gestation delay and memory period, along with nonlocal competition, play key roles in controlling population density and maintaining the stability of ecosystems. To control the population density of the Dendrolimus superans, which causes significant damage to forests, we propose a pest control system incorporating both two delays and nonlocal competition considering Holling II type functional response. We analyze the conditions for the existence of Hopf bifurcation and derive the normal form of Hopf bifurcation using multiple time scales method. Considering the biological significance, we employ appropriate parameters for numerical simulations. Furthermore, we find that varying habitat complexity parameters leads to different moduli of bifurcation periodic solutions. Especially, both two delays contribute to maintaining the stability of steady states.
subject: Articles
  topic: section
subject: Pest control model
  topic: keywords
subject: two delays
  topic: keywords
subject: Hopf bifurcation
  topic: keywords
subject: nonlocal competition
  topic: keywords
subject: habitat complexity
  topic: keywords
creator: Xu Wen
creator: Yuting Ding
rights: Copyright (c) 2025 Journal of Nonlinear Modeling and Analysis
date: 2025-11-26
publication date: 2025-11-26
starting page: 2157
ending page: 2181
doi: 10.12150/jnma.2025.2157

A New Approach to Hermite-Hadamard-Type Inequality with Proportional Caputo-Hybrid Operator
type: item
description: Fractional calculus plays a crucial role in mathematics and applied sciences as it extends classical analysis, overcoming many of its constraints. Moreover, using the innovative hybrid fractional operator, which merges the proportional and Caputo operators, is beneficial in numerous domains of computer science and mathematics. In this study, we focus on the proportional Caputo-hybrid operator due to its wide range of applications. Firstly, we present a new extension of Hermite-Hadamard-type inequalities for the proportional Caputo-hybrid operator and derive an identity. Then, utilizing this novel generalized identity, we establish significant integral inequalities associated with the right-hand side of Hermite-Hadamard-type inequalities for the proportional Caputo-hybrid operator. Furthermore, we provide illustrative examples accompanied by the graphs to demonstrate the newly established inequalities.
subject: Articles
  topic: section
subject: Hermite-Hadamard-type inequalities
  topic: keywords
subject: trapezoid-type inequalities
  topic: keywords
subject: convex functions
  topic: keywords
subject: proportional Caputo-Hybrid operator
  topic: keywords
creator: İzzettin Demir
creator: Tuba Tunç
creator: Mehmet Zeki Sarıkaya
rights: Copyright (c) 2025 Journal of Nonlinear Modeling and Analysis
date: 2025-11-26
publication date: 2025-11-26
starting page: 2137
ending page: 2156
doi: 10.12150/jnma.2025.2137