Discrete Prey–Predator Model with Square Root Functional Response Under Imprecise Biological Parameters

Abstract

This paper presents a discrete-time prey–predator model in which the prey exhibits herd behavior, and hence, the predator interacts along the outer corridor of the herd of the prey. Due to the unavailability of numerical information of the biological parameters, we consider the model with interval parameters in the parametric functional form. The existence and stability of the proposed model are analyzed. We give a flip bifurcation analysis and chaos control procedure. The bifurcation diagrams, phase portraits and time graphs are presented for different model parameters. Here, we introduce a new concept in bifurcation analysis. The codimension of a bifurcation is the number of parameters which must be varied for the bifurcation to occur. When we consider p as bifurcation parameter, ultimately, we consider here 4 bifurcation parameter in a certain range, but interesting fact is that using our technic, we convert this 4 codim bifurcation in 1 codim. Numerical simulations exhibit that the present model is a chaotic with rich dynamics.