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Turing instability of periodic solutions for a general Brusselator model with nonlinear diffusion

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  • Zhang, Panpan
  • Wu, Kuilin

Abstract

This paper focus on a general Brusselator model with diffusion. In addition to the fact that both self-diffusion and cross-diffusion can induce Turing instability for Brusselator model, we aim to investigate the instability phenomena of nonlinear diffusion on stable periodic solutions bifurcating from equilibrium. We establish a diffusion rate formula in terms of the diffusion coefficients to determine Turing instability of periodic solutions. Based on Implicit Function Theorem and Floquet theory, the conditions of Turing instability of periodic solutions are provided. Finally, we show an example and provide numerical simulations to illustrate our results.

Suggested Citation

  • Zhang, Panpan & Wu, Kuilin, 2025. "Turing instability of periodic solutions for a general Brusselator model with nonlinear diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 201(P3).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p3:s0960077925013906
    DOI: 10.1016/j.chaos.2025.117377
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