Mathematical modeling of cyclic population dynamics

A. Bayliss*, A. A. Nepomnyashchy, V. A. Volpert

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


A rock–paper–scissors three species cyclic ecosystem is considered. Deterministic mathematical models based on delayed ODEs and nonlocal PDEs are proposed and studied both analytically and numerically. Transitions between the coexistence state that is associated with biodiversity, limit cycles and the heteroclinic cycle are discussed for the ODE model. Traveling waves between the coexistence state and single species states are studied for the PDE model. We show that delay promotes oscillatory instabilities of the coexistence state while nonlocality promotes stationary cellular instabilities.

Original languageEnglish (US)
Pages (from-to)56-78
Number of pages23
JournalPhysica D: Nonlinear Phenomena
StatePublished - Jul 2019


  • Cyclic ecosystems
  • Delay equations
  • Heteroclinic cycle
  • Nonlocality
  • Population dynamics
  • Traveling wave

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Applied Mathematics
  • Statistical and Nonlinear Physics
  • Mathematical Physics


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