Approximate Analytical Approach to Nonlinear System of Prey Predator Models

Abstract

Many biological problems can be reduced to the description of a food chain model or a newlinefood web. In these systems, the biodiversity and coexistence of all species are vital issues. newlineThree ecological models have been proposed in the case of the existence of a reserved area, newlinein order to understand multi-species interactions so as to prevent the slow extinction of some newlineendangered species and to test the stability of the models when the length of the food chain newlineand size of the web are increased. newlineIn the first model of the fourth chapter, a nonlinear mathematical model is proposed and newlineanalysed to study the effects of top predator interference on the dynamics of a food chain newlinemodel. The mathematical model is formulated using a system of non-linear ordinary differential newlineequations. In this model, there are three state-dimensionless variables: the size of newlinethe prey population, the size of the intermediate predator and the size of the top predator newlinepopulation. The analytical results are compared with the numerical simulation using MATLAB newlinesoftware and satisfactory results are noticed newline