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

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.

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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\textit{S. Tang} and \textit{L. Chen}, Chaos Solitons Fractals 13, No. 4, 875--884 (2002; Zbl 1022.92042)

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