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Zbl 0934.92027
Sáez, E.; González-Olivares, E.
Dynamics of a predator-prey model. (English)
[J] SIAM J. Appl. Math. 59, No.5, 1867-1878 (1999). ISSN 0036-1399; ISSN 1095-712X/e

Summary: We describe the bifurcation diagram of limit cycles that appear in the first realistic quadrant of the predator-prey model proposed by {\it 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 2000:: *92D25 Population dynamics
34C05 Qualitative theory of some special solutions of ODE
37N25 Dynamical systems in biology
92D40 Ecology

Keywords: limit cycles; bifurcations; predator-prey models

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