Dynamic Analysis of a Predator and Prey Model with Some Computational Simulations

TL;DR

This paper develops a predator-prey model using nonlinear differential equations, introduces a homotopy technique for approximate solutions, and employs sensitivity analysis to identify key parameters, supported by numerical simulations.

Contribution

It proposes a novel homotopy method with expanding parameters for analytical approximation and applies local sensitivity analysis to ecological predator-prey models.

Findings

Homotopy technique yields approximate solutions for the model.

Sensitivity analysis identifies critical parameters affecting dynamics.

Numerical simulations validate the analytical approaches.

Abstract

Mathematical modelling and numerical simulations of interaction populations are crucial topics in systems biology. The interactions of ecological models may occur among individuals of the same species or individuals of different species. Describing the dynamics of such models occasionally requires some techniques of model analysis. Choosing appropriate techniques of model analysis is often a difficult task. We define a prey (mouse) and predator (cat) model. The system is modelled by a pair of non-linear ordinary differential equations using mass action law, under constant rates. A proper scaling is suggested to minimize the number of parameters. More interestingly, we propose a homotopy technique with n expanding parame- ters for finding some analytical approximate solutions. Furthermore, using the local sensitivity method is another important step forward in this study because it helps to identify critical model parameters. Numerical simulations are provided using Matlab for different parameters and initial conditions.