Bifurcation Analysis of Predator-Prey System using Conformable Fractional Order Discretization

TL;DR

This paper applies conformal fractional order discretization to analyze bifurcations and stability in a predator-prey system, revealing complex dynamics and bifurcation phenomena with implications for ecological management.

Contribution

It introduces a novel discretization method that preserves fractional-order dynamics, enabling detailed bifurcation and stability analysis of predator-prey models.

Findings

Identification of period-doubling bifurcations

Detection of Neimark-Sacker bifurcations

Insights into parameter effects on system stability

Abstract

In this paper, conformal fractional order discretization [20, 24, 25] is used to analyze bifurcation analysis and stability of a predator-prey system. A continuous model has been discretized into a discrete one while preserving the fractional-order dynamics. This allows us to look more closely at the stability properties of the system and bifurcation phenomena, including period-doubling and Neimark-Sacker bifurcation. Through numerical and theoretical methods, this research investigated how the modification in system parameters affects the overall dynamics, which may have implications for ecological management and conservation strategies.