Bifurcation Analysis of a Discrete Food Chain Model with Harvesting

Abdul Qadeer Khan,Shahid Mehmood Qureshi,Baogui Xin

doi:10.1155/2021/5987435

Abdul Qadeer Khan, Shahid Mehmood Qureshi + Show 1 more

Open Access

https://doi.org/10.1155/2021/5987435

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Abstract

We explore existence of fixed points, topological classifications around fixed points, existence of periodic points and prime period, and bifurcation analysis of a three-species discrete food chain model with harvesting. Finally, theoretical results are numerically verified.

Highlights

Many different types of interactions exist in nature between various species of organisms on this planet Earth and are studied under the discipline of ecology
Ammensalism is a type of ecological interactions between the members of two different species in which one is harmed, destroyed, or inhabited by the member of another species, while the other remains unaffected, neither harmed nor benefitted
It is a type of competitive behavior among different species and is frequently used to refer to asymmetrical competitive association

Summary

Introduction

Many different types of interactions exist in nature between various species of organisms on this planet Earth and are studied under the discipline of ecology. Many researchers have investigated the dynamical properties of discrete-time ecological models such as prey-predation, competitions, neutralism, and mutualism by studying fixed points, local and global attractivity, bounded, existence of bifurcation, and many more. D)yn+dσyn− 1) On the contrary, in recent years, many papers have been published to investigate the bifurcation analysis of certain discrete models by choosing step size as a bifurcation parameter. Motivated from the aforementioned studies, in this work, we explore existence of fixed points, topological classifications around fixed points, periodic points, and bifurcation analysis, by choosing step size h as a bifurcation parameter, of the following three species discrete food chain model with harvesting: xn+1 xn + h􏼐a1 1 − k1􏼁xn − α11x2n􏼑, yn+1 yn + h􏼐a2 1 − k2􏼁yn − α22y2n − α21xnyn􏼑, (15).

Study of Equilibrium Points

Dynamical Behavior

Periodic Points

Analysis of Bifurcation

Numerical Simulations