Chaotic Dynamics of the Fractional Order Predator-Prey Model Incorporating Gompertz Growth on Prey with Ivlev Functional Response

Year 2024, Volume: 6 Issue: 3, 192 - 204, 31.07.2024

Md. Jasim Uddin , P. K. Santra , Sarker Md Sohel Rana , G.s. Mahapatra

https://doi.org/10.51537/chaos.1300754

Abstract

This paper examines dynamic behaviours of a two-species discrete fractional order predator-prey system with functional response form of Ivlev along with Gompertz growth of prey population. A discretization scheme is first applied to get Caputo fractional differential system for the prey-predator model. This study identifies certain conditions for the local asymptotic stability at the fixed points of the proposed prey-predator model. The existence and direction of the period-doubling bifurcation, Neimark-Sacker bifurcation, and Control Chaos are examined for the discrete-time domain. As the bifurcation parameter increases, the system displays chaotic behaviour. For various model parameters, bifurcation diagrams, phase portraits, and time graphs are obtained. Theoretical predictions and long-term chaotic behaviour are supported by numerical simulations across a wide variety of parameters. This article aims to offer an OGY and state feedback strategy that can stabilize chaotic orbits at a precarious equilibrium point.

Keywords

Prey-predator model, Fractional order, Bifurcations, Maximum Lyapunov Exponents, Fractal dimensions, Chaos control

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