Turing Instability of Periodic Solutions for a General Degn–Harrison Model with Cross-Diffusion

• Gaihui Guo ^[1] ; Wangrui Li ^[1] ; Yanfei Du ^[1] ; Sajad Jafari ^[2]
  1. [1] Shaanxi University of Science and Technology

     Shaanxi University of Science and Technology

     China

     
  2. [2] Amirkabir University of Technology

     Amirkabir University of Technology

     Irán

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 2, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • A general Degn–Harrison model with cross-diffusion is investigated under Neumann boundary conditions. How the cross-diffusion destabilizes the stable periodic solutions originating from the unique positive equilibrium is fully investigated. By the implicit function theorem and Floquet theory, we propose some conditions on crossdiffusion coefficients, under which these stable periodic solutions become unstable.

    The destabilization gives rise to the development of new irregular spatiotemporal patterns. We also show some numerical simulations to further support the theoretical analysis results.

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