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<p>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 cross-diffusion 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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年3月5日

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  • Gaihui Guo,
  • Wangrui Li,
  • Yanfei Du,
  • Sajad Jafari

摘要

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 cross-diffusion 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.