Co-existence of a Period Annulus and a Limit Cycle in a Class of Predator-Prey Models with Group Defense

Robert E. Kooij*, André Zegeling

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
4 Downloads (Pure)


For a family of two-dimensional predator-prey models of Gause type, we investigate the simultaneous occurrence of a center singularity and a limit cycle. The family is characterized by the fact that the functional response is nonanalytical and ehibits group defense. We prove the eistence and uniqueness of the limit cycle using a new theorem for Liénard systems. The new theorem gives conditions for the uniqueness of a limit cycle which surrounds a period annulus. The results of this paper provide a mechanism for studying the global behavior of solutions to Gause systems through bifurcation of an integrable system which contains a center and a limit cycle.

Original languageEnglish
Article number2150154
Number of pages1
JournalInternational Journal of Bifurcation and Chaos
Issue number10
Publication statusPublished - 2021

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • bifurcation
  • functional response
  • Generalized Gause model
  • limit cycle


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