Dynamic Complexities in Predator-Prey Ecosystem Models with Functional Response

Natural populations whose generations are non-overlapping can be modelled by difference equations that describe how the population evolves in discrete time-steps. In the 1970s ecological research detected chaos and other forms of complex dynamics in simple population dynamics models, initiating a new research tradition in ecology. However, in former studies most of the investigations of complex population dynamics were mainly concentrated on single populations instead of higher dimensional ecological systems. This paper reports a recent study on the complicated dynamics occurring in class of discrete-time models of predator-prey interaction, Beddington-DeAngelis functional response and Monod-Haldane or Holling type IV functional response are applied to these predator-prey models. The complexities include (a)chaotic bands with periodic windows, pitchfork and tangent bifurcations, (b) attractor crises, (c) chaotic attractors, (d) intermittency,(e) supertransients, and (f) periodic doubling cascade.