Stability and bifurcation analysis of a discrete prey–predator model with sigmoid functional response and Allee effect

Abstract

In this paper, we have considered a discrete-time predator–prey model with sigmoid functional response and Allee effect. We have discussed the conditions of existence of the feasible fixed point. The stability criterion of the fixed point carried out algebraically. Analytically we have shown that the system undergoes flip and Neimark–Sacker bifurcations. We also analyzed Neimark–Sacker bifurcation by center manifold theorem taking discretization factor(generation gap) as a bifurcation parameter. Under a parametric condition, all the bifurcation phenomena and chaotic features have been justified numerically. Finally, we use the hybrid control strategy to control flip and Neimark–Sacker bifurcations.