Bifurcation Analysis and Chaos Control for a Discrete Fractional-Order Prey–Predator System

Allee effect relates to the fitness of an individual and the density of the population in an ecosystem. This type of positive association may lead to a population size below which the persistence of the species is not possible. In this work, we consider a fractional-order discrete-time system representing interactions of predator and prey involving Holling type II response and Allee effect. The existence results of the equilibrium points together with the stability of the system are discussed. The chaotic behavior of the system is analyzed with the bifurcation theory to prove the existence of periodic doubling and Neimark–Sacker bifurcations. The control strategy are employed to the system to study the containment of the chaos and simulations are performed to support the results.