Stability and bifurcation analysis of a discrete fractional order predator-prey Leslie-Gower model with fear effect, Allee effect, and interspecies rivalry

Abstract

This paper discusses the analysis of a discrete fractional-order Leslie-Gower model with fear effects, Allee effects, and interspecies competition. The discrete model is obtained by discretizing the continuous model using the piecewise constant approximation method. The model has four fixed points, namely trivial fixed point, prey extinction fixed point, predator extinction fixed point, and interior fixed point. The trivial fixed point always exists, while the existence of prey extinction, predator extinction, and interior fixed points are determined by certain conditions. The stability analysis shows that there are topological differences that depend on the parameter and the size of the integration step. Bifurcation analysis is performed using center manifold theory and bifurcation theorem. By choosing the integration step as the bifurcation parameter, it can be shown that the model experiences period-doubling bifurcation and Neimark-Sacker bifurcation. Numerical simulations are carried out at the end of this paper to confirm the analytical results.