Fast–Slow Dynamics for Intraguild Predation Models with Evolutionary Effects

Jianhe Shen, Cheng Hsiung Hsu, Ting Hui Yang

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


This work is concerned with the fast–slow dynamics for intraguild predation models with evolutionary effects. Assuming the survival pressure of the weaker predator induces evolution of it to the intraguild predator, then the system can be viewed as a singularly perturbed problem with two different time scales—predation time scale and evolution time scale. Using the geometric singular perturbation theory, we first completely analyze the limiting slow–fast dynamics of the system which involve the existence of turning points. Then, an application of the geometric singular perturbation theory gives rise to the birth of relaxation oscillations caused by the turning points and the associated delay of stability loss. From our main results, one can see that evolution enhances survival rates of inferior competitors.

Original languageEnglish
Pages (from-to)895-920
Number of pages26
JournalJournal of Dynamics and Differential Equations
Issue number2
StatePublished - 1 Jun 2020


  • Delay of stability loss
  • Delayed bifurcation
  • Geometric singular perturbation theory
  • Intraguild predator
  • Relaxation oscillation
  • Transcritical bifurcation
  • Turning points


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