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Volume 6,     Number 2,     Summer 1998

 

UNIQUENESS OF LIMIT CYCLES FOR A
PREDATOR-PREY SYSTEM OF
HOLLING AND LESLIE TYPE
SZE-BI HSU AND TZY-WE1 HWANG

Abstract. In this paper we study the uniqueness of limit cycles of the Holling-Tanner model, an important predatorprey model in mathematical ecology. We first transform the system into a predator-prey system with Gause-type. The reduced system is different from the classical one since the prey isocline has two humps instead of one. We use the method of reflections to estimate the Floquet exponent of the limit cycle and derive a sufficient condition for the uniqueness of limit cycles.

 

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