Bifurcation Analysis of Predator-Prey System using Conformable Fractional Order Discretization
Muhammad Rafaqat, Abubakar Masha, Nauman Ahmed, Ali Raza, Wojciech Sumelka
TL;DR
The paper addresses stability and bifurcation analysis of a predator-prey system using a conformable fractional-order discretization that preserves fractional dynamics. It derives a discrete-time fractional model, locates the positive fixed point $E^*=(\frac{d}{b},\frac{(b-d)r}{b^{2}})$, and analyzes the Jacobian to obtain Neimark–Sacker and flip (period-doubling) bifurcation conditions via center-manifold reduction and normal-form techniques, including explicit regions $A_{NS}$ and $A_{PD}$. A hybrid chaos-control scheme with a parameter $\beta$ is proposed to stabilize the system, with stability certified by Jury conditions on the controlled Jacobian. Numerical experiments corroborate NS and PD scenarios and demonstrate chaos suppression, offering a rigorous framework for controlling complex dynamics in fractional-order ecological models with potential ecological-management applications.
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.