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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.

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