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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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##### References:
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