Global Stability Analysis And Numerical Simulation For Nonlinear Ecological Model With Delay

Abstract

Discrete models are particularly useful for modelling population dynamics when the population size remains small over several generations or when it is relatively constant within a single generation. We focus on finding effective solutions to the challenges posed by such populations. In our research, we have successfully used qualitative analytic techniques to study a three species model. It is important to consider the reproductive process and other population dynamics as happening in real-time, even for species with unclear reproductive seasons. While the delay technique has introduced some complexities, we have identified sufficient conditions to address them. Our study examines the global stability of a three species ecological model that does not consider delayed intraspecific competition. We analyze a delayed Lotka Volterra system, which demonstrates global stability when the interaction matrix is effective. We present numerical simulations to illustrate the theoretical results of the delay differential equation. Since delay differential equation models are always challenging to solve, we propose the use of JiTCDDE (just-in-time compilation for delay differential equations) of the DDE integration method to solve the dynamical three species models.