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Existence of multiple limit cycles in a predator-prey model with \(\arctan(ax)\) as functional response. (English) Zbl 1320.92073
Summary: We consider a Gause type predator-prey system with functional response given by \(\theta(x)=\arctan(ax)\), where \(a > 0\), and give a counterexample to the criterion given in [B. S. Attili and S. F. Mallak, ibid. 1, No. 1, 33–40 (2006; Zbl 1121.92064)] for the nonexistence of limit cycles. When this criterion is satisfied, instead this system can have a locally asymptotically stable coexistence equilibrium surrounded by at least two limit cycles.

MSC:
92D25 Population dynamics (general)
92D40 Ecology
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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Full Text: Euclid