Uniqueness of the limit cycle for Gause-type predator-prey systems
The author gives two theorems ensuring that a generalized Gause-type predator-prey system possesses no and at most one (and then stable) limit cycle, respectively. The latter theorem covers the criterion for the uniqueness of limit cycles given by \textit{S. H. Ding} [SIAM J. Math. Anal. 20, No. 6, 1426-1435 (1989; Zbl 0678.92013)] and \textit{X.-C. Huang} and \textit{S. J. Merrill} [Math. Biosci. 96, No. 1, 47-60 (1989, Zbl 0676.92008)] as a special case. Two examples of predator-prey dynamics are presented as illustrations.
scientific article; zbMATH DE number 1354757
scientific article