Bifurcations and chaos control for a discrete fractional-order Leslie-Gower model incorporating fear in predators and Allee effect in prey

In this research, we analyze a discrete-time fractional-order modified Leslie-Gower predator-prey model that incorporates the Allee effect on prey and the fear effect on predators. The findings demonstrate complex dynamic behaviors resulting from these elements. First, we show the existence of equilibrium points and the conditions for their stability. Moreover, the incorporation of Allee and fear effects leads to various bifurcations, such as Neimark-Sacker and flip bifurcations. We perform numerical simulations with different values of the fractional parameter $q$ to illustrate the complex temporal dynamics of the model. The theoretical results are corroborated and confirmed through numerical simulations.