Periodic solutions for a 3 × 3 competitive system with cross-diffusion

Salomé Martínez, Wei-Ming Ni

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


In this paper we study the role of cross-diffusion in the existence of spatially non-constant periodic solutions for the Lotka-Volterra competition system for three species. By properly choosing cross-diffusion coefficients, we show that Hopf bifurcation occurs at a constant steady state. Furthermore, these spatially nonhomogeneous periodic solutions are stable if diffusion rates are in appropriate ranges.

Original languageEnglish (US)
Pages (from-to)725-746
Number of pages22
JournalDiscrete and Continuous Dynamical Systems
Issue number3
StatePublished - Jul 1 2006


  • 3 × 3 competitive system
  • Cross-diffusion
  • Periodic solutions


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