Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities. (English) Zbl 0756.92026

Summary: A classical predator-prey model is considered with reference to the case of periodically varying parameters. Six elementary seasonality mechanisms are identified and analysed in detail by means of a continuation technique producing complete bifurcation diagrams. The results show that each elementary mechanism can give rise to multiple attractors and that catastrophic transitions can occur when suitable parameters are slightly changed.
Moreover, the two classical routes to chaos, namely, torus destruction and cascade of period doublings, are numerically detected. Since in the case of constant parameters the model cannot have multiple attractors, catastrophes and chaos, the results support the conjecture that seasons can very easily give rise to complex population dynamics.


92D40 Ecology
37N99 Applications of dynamical systems
37G99 Local and nonlocal bifurcation theory for dynamical systems
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