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Absence of limit cycles of a predator-prey system with a sigmoid functional response. (English) Zbl 0865.34032
Summary: A large number of studies have been made on the predator-prey system with Holling’s functional response, namely, \(\phi(x)=x^n/(a+x^n)\) \((n=1,2)\). This paper presents a sufficient condition under which the predator-prey system has no limit cycles for \(n=3\). The argument used here is based on a result of Liénard dynamics. The relation between previous results \((n=1,2)\) and our result \((n=3)\) is cleared. Some phase portraits of trajectories of the predator-prey system are also given as an example of our result.

MSC:
34C25 Periodic solutions to ordinary differential equations
92D25 Population dynamics (general)
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