Chaos in a Hybrid Food Chain Model

Safaa Jawad Ali,Abed Almohsen Naji Almohasin,Raid Kamel Naji,Adwea Naji Atewi,Norihan Md Arifin

doi:10.24996/ijs.2021.62.7.25

Abstract

In this paper, chaotic and periodic dynamics in a hybrid food chain system with Holling type IV and Lotka-Volterra responses are discussed. The system is observed to be dissipative. The global stability of the equilibrium points is analyzed using Routh-Hurwitz criterion and Lyapunov direct method. Chaos phenomena is characterized by attractors and bifurcation diagram. The effect of the controlling parameter of the model is investigated theoretically and numerically.

Highlights

Nonlinear phenomena play important rules in design systems of engineering and structures
Upadhyay et al [19] proposed and studied a tritrophic food chain model with Sokol-Howell functional response, incorporating the multiple gestation time delays. They explored the existence of various dynamical structures, such as Hopf-bifurcation, periodic solutions, and chaotic dynamics
The food chain model is modified to the food chain model studied in [9], so that it involves Lotka-Volterra type of functional response in the second and third levels, instead of Holling type-II functional response that was used in the previous work

Summary

Introduction

Nonlinear phenomena play important rules in design systems of engineering and structures. Upadhyay et al [19] proposed and studied a tritrophic food chain model with Sokol-Howell functional response, incorporating the multiple gestation time delays They explored the existence of various dynamical structures, such as Hopf-bifurcation, periodic solutions, and chaotic dynamics. The food chain model is modified to the food chain model studied in [9], so that it involves Lotka-Volterra type of functional response in the second and third levels, instead of Holling type-II functional response that was used in the previous work. The idea of such modification comes from the fact of availability of food at the second level in the environment. The second reason for such modification is that we want to reduce the intensity of nonlinearity in the system and study the effects of such reduction on the existence of chaos

The Mathematical Model

Conclusions