Multiplicity and Stability of Equilibrium States of Three-Dimensional Nonlinear System (Journal of Nonlinear Modeling and Analysis, 2024)
The multiplicity and stability of the equilibrium states of a three-dimensional differential system with initial conditions and three cross terms are studied in this paper. The existence and multiplicity of equilibrium states are given under the different qualifications of parameters. Besides, the local stability of the equilibrium state is shown by analyzing the eigenfunction of the Jacobi matrix. The global stability of the equilibrium state is obtained by constructing the Lyapunov function. Furthermore, the numerical simulation intuitively reflected the relationship of variables and verified the correctness of theoretical analysis.
Keywords: Equilibrium states; multiplicity; local stability; global stability; numerical simulation.