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Abstract
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This paper is a study of one of the most beautiful phenomena in dynamical system: Limit
Cycle. In mathematics, in the study of dynamical systems with two-dimensional phase space,
a limit cycle is a closed trajectory in phase space having the property that at least one other
trajectory spirals into it as time approaches either positive or negative infinity. In this paper, nonexistence of limit cycles for two classes of predator-prey systems will be studied. We give some sufficient conditions for nonexistence of limit cycles for predator-prey systems.
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