Chaos in functional response host–parasitoid ecosystem models

Natural populations whose generations are non-overlapping can be modeled 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, the investigations of complex population dynamics have mainly concentrated on single populations and no higher-dimensional ecological systems. In this study, in order to simulate cyclic effects due to changes in parasitoidʹs behavior, Holling type II and III functional response functions are applied to host–parasitoid models, respectively. For each model, the complexities include (1) chaotic bands with periodic windows, pitchfork and tangent bifurcations, and attractor crises, (2) non-unique dynamics, meaning that several attractors coexist, (3) intermittency, and (4) supertransients.