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Dynamics of a predator-prey model. (English) Zbl 0934.92027

Summary: We describe the bifurcation diagram of limit cycles that appear in the first realistic quadrant of the predator-prey model proposed by R.M. May [ Stability and complexity in model ecosystems. (1974)]. In particular, we give a qualitative description of the bifurcation curve when two limit cycles collapse on a semistable limit cycle and disappear. Moreover, we show that local asymptotic stability of a positive equilibrium point does not imply global stability for this class of predator-prey models.

MSC:

92D25 Population dynamics (general)
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
37N25 Dynamical systems in biology
92D40 Ecology
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