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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.

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