Dynamics of q deformed Ricker map

Abstract

We apply the deformation scheme to the classical Ricker map and obtain a q-deformed Ricker map, namely, q-Ricker map. The aim of the paper is to investigate the nonlinear dynamics, bifurcation structure, and topological entropy of q-Ricker map. In particular, we show that q-Ricker map proclaims many exciting phenomena that are remarkable in one-dimensional dynamical systems, such as the presence of coexisting attractors, physically non-observable chaos, hydra paradox, bubbling effect, and extinction. We discuss fold and flip bifurcations and further the presence of stochastically stable chaos. Finally, we show that a certain amount of deformation in the system can keep it in equilibrium; however, excessive deformation causes extinction.