Chaos in functional response host - parasitoid ecosystem models. (English) Zbl 1022.92042

Tang, Sanyi; Chen, Lansun

Chaos Solitons Fractals 13, No. 4, 875-884 (2002).

Summary: 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 not higher-dimensional ecological systems.
In this study, in order to simulate cyclic effects due to changes in parasitoid’s 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.

MSC:

92D40	Ecology
92D25	Population dynamics (general)
37N25	Dynamical systems in biology
39A05	General theory of difference equations

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