Conditions for uniqueness of limit cycles in general predator-prey systems

  • Huang X
  • Merrill S
  • 2

    Readers

    Mendeley users who have this article in their library.
  • 36

    Citations

    Citations of this article.

Abstract

Using a transformation to a generalized Lienard system, theorems are presented that give conditions under which unique limit cycles for generalized ecological systems, including those of predator-prey form, exist. The generalized systems contain those studied by Rosenzweig and MacArthur (1963); Hsu, Hubbell, and Waltman (1978); Kazarinnoff and van den Driessche (1978); Cheng (1981); Liou and Cheng (1987); and Kuang and Freedman (1988). Although very similar in approach to the result presented by Kuang and Freedman, the conditions presented here are of simpler form and in terms of the original (untransformed) functions. The results also apply to more general growth terms for the prey as shown in the examples provided. In particular, an immigration term is allowable. © 1989.

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

  • Xun Cheng Huang

  • Stephen J. Merrill

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free