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Multiple focus and Hopf bifurcations in a predator-prey system with nonmonotonic functional response. (English) Zbl 1109.34034
A two-dimensional predator prey system is studied that has been considered earlier in {\it H. Zhu, S. A. Campbell} and {\it G. S. K. Wolkowicz} [SIAM J. Appl. Math. 63, No. 2, 636--682 (2002; Zbl 1036.34049)]. The case is followed up this time when the system has a weak stable focus. The order of the focus is established and conditions are given under which the system has two limit cycles around it, a stable and an unstable one.

MSC:
34C25Periodic solutions of ODE
37G15Bifurcations of limit cycles and periodic orbits
37N25Dynamical systems in biology
92D25Population dynamics (general)
34C23Bifurcation (ODE)
34C60Qualitative investigation and simulation of models (ODE)
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