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Uniqueness of limit cycles in Gause-type models of predator-prey systems. (English) Zbl 0642.92016
Summary: This paper deals with the question of uniqueness of limit cycles in predator-prey systems of Gause type. By utilizing several transformations, these systems are reduced to a generalized Lienard system as discussed by L. A. Cherkas and L. I. Zhilevich [Differ. Uravn. 6, 1170-1178 (1970; Zbl 0213.364)] and by Z. Zhang [Appl. Anal. 23, 63-76 (1986; Zbl 0582.34038)]. As a consequence, criteria for the uniqueness of limit cycles are derived, which include results of K.-S. Cheng [SIAM J. Math. Anal. 12, 541-548 (1981; Zbl 0471.92021)] and are related to results of L.-P. Liou and K.-S. Cheng (to appear). Several examples are given to illustrate our results.

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