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On a predator-prey system of Holling type. (English) Zbl 0868.34023
Summary: We consider a predator-prey system with a fairly general functional response of Holling type and give a necessary and sufficient condition under which this system has exactly one stable limit cycle. Our result extends previous ones and is an answer to a conjecture which was recently presented by J. Sugie, K. Miyamoto and K. Morino [Appl. Math. Lett. 9, No. 4, 85-90 (1996; Zbl 0865.34032)].

MSC:
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
70K05 Phase plane analysis, limit cycles for nonlinear problems in mechanics
92D25 Population dynamics (general)
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
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