Qualitative Behavior for a Discretized Conformable Fractional-Order Lotka-Volterra Model With Harvesting Effects

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DOI: https://doi.org/10.28924/2291-8639-22-2024-51
Published: Mar 18, 2024
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Messaoud Berkal, Juan F. Navarro, M. B. Almatrafi, Qualitative Behavior for a Discretized Conformable Fractional-Order Lotka-Volterra Model With Harvesting Effects, Int. J. Anal. Appl., 22 (2024), 51.

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Messaoud Berkal, Juan F. Navarro, M. B. Almatrafi

Abstract

The predator-prey model is a widely mathematical structure that explains the dynamics between two interacting populations: predators and prey. The predator-prey interaction represents a fundamental dynamic in nature, influencing the stability and balance of ecosystems worldwide. The purpose of this article is to provide insight into the complex interactions and feedback mechanisms between predators and prey in ecological systems via mathematical tools such as stability and bifurcation. We investigate a fractional-order Lotka-Volterra model with a harvesting effect using stability and bifurcation theory. The equilibrium points and local stability of the purposed model are presented in this article. The bifurcation analysis, which is a potent approach used to analyse the qualitative behavior of the predator-prey system as the parameter values are varied, is also explored. In particular, a Neimark-Sacker bifurcation and a period-doubling bifurcation are theoretically and numerically examined. Furthermore, we illustrate some 2D figures to show the phase portriat and bifurcations of this model at various points.

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