Stability Analysis and Bifurcation Control of a Fractional Order Predator Prey System

Fractional-order predator–prey models provide superior ecological fidelity by capturing intrinsic memory effects. However, the fractional derivative order introduces an additional dimension to parameter space, which is unexplored in existing dynamical analyses. This paper delves into the bifurcation behaviors of a two-dimensional fractional-order predator–prey model, taking into account the maturation period of larvae. By utilizing time delay as the bifurcation parameter, the characteristic equation is analyzed to derive conditions for stability and bifurcation. Meanwhile, the introduction to fractional-order theory endows the predator–prey system with improved historical dependence. The relationship between order and bifurcation behavior in the fractional-order predator–prey model is discussed in simulation experiments, which provides a reference for the establishment of the fractional-order system. Additionally, this paper introduces a controller to control the bifurcation behavior through feedback-gain parameters. Simulation results not only exhibit the dynamic characteristics of fractional-order models, but also demonstrate the success of controllers over bifurcation behaviors.