Work

Dynamics of the system of delay differential equations with nonlinearity having a simple behavior at infinity

Year: 2024

Type: article

Abstract: In this paper, we study the dynamics of a system of nonlinear differential equations with delay. We find stable equilibrium states and regions of attraction to them in the phase space of the system, as well as stable and unstable homogeneous and inhomogeneous cycles. We find conditions on the parameters of the system for multistability. We show that the coupling parameter has a decisive influence on the dynamics of the system. We find regions of the parameters of the system and extensive sets of initial conditions such that if we take these values of the parameters and any initial conditions from these sets, the system will have simple dynamics.

Source: Partial Differential Equations in Applied Mathematics

DOI: 10.1016/j.padiff.2024.100934

Authors: A.A. Kashchenko, I.S. Luzin

Institution: Yaroslavl State University

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,230

Funders: Ministry of Education and Science of the Russian Federation, Russian Science Foundation