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

Sáez, E.; González-Olivares, E.

SIAM J. Appl. Math. 59, No. 5, 1867-1878 (1999).

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

Keywords:

limit cycles; bifurcations; predator-prey models