Allee effect and Holling type - II response in a discrete fractional order prey - predator model

Abstract

A gauss type prey - predator model is considered with Allee effect and Holling type II response. Fractional order two species system is discretized. The discretized system exhibits much richer and complex dynamics than its corresponding continuous version.Bifurcation types like flip, neimark sacker and chaos exist in the discretized system.Existence of the positive fixed points is established and local stability of discrete fractional order system is discussed with the variational matrix. It is also shown that the system allows a flip bifurcation and a neimark - sacker bifurcation. Rich dynamical nature of the system is established through time plots with phase trajectory, exciting invariant circles and periodic doubling bifurcation which leads to chaos.