Qualitative behavior of a discrete predator–prey system under fear effects

Abstract

Abstract Numerous field data and experiments on the perching birds or songbirds show that the fear of predators can cause significant changes in the prey population. Fear of predatory populations increases the chances of survival of the prey population, and this can greatly reduce the reproduction of the prey population. The influence of fear has contributed a leading role in both the environmental biology and theoretical ecology. Taking into account the interaction of predator–prey with non-overlapping generations, a discrete-time model is proposed and studied. Keeping in mind the biological feasibility of species, the existence of fixed points is studied along with the local asymptotic behavior of the proposed model around these fixed points. Furthermore, taking into account the oscillatory behavior of the model, various types of bifurcations are analyzed about biologically feasible fixed points with an application of center manifold theory and bifurcation theory of normal forms. Existence of chaos is discussed, and fluctuating and chaotic behavior of the system is controlled through implementation of different chaos control procedures. The illustration of theoretical discussion is carried out via validation of observed experimental field data and appropriate numerical simulation.