Scholarlink

<p>This work examines Turing instability and pattern formation in a predator-prey system incorporating fear effects and super cross-diffusion. We first establish stability criteria for equilibrium states both with and without super cross-diffusion, demonstrating that cross-diffusion can destabilize otherwise stable equilibria. Linear stability analysis subsequently derives precise conditions for Turing instability, revealing cross-diffusion as the fundamental mechanism driving spatial pattern emergence. Using the cross-diffusion coefficient as a bifurcation parameter, we employ weakly nonlinear theory to derive amplitude equations governing excited modes near the Turing bifurcation threshold. Dynamical analysis of these equations elucidates structural transitions and stability properties across diverse Turing pattern formations. Theoretical predictions are validated through comprehensive numerical simulations.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Pattern Formation by Super Cross-Diffusion in a Fractional-Order Predator-Prey Model with Fear Effect

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年2月25日

查看全文
  • Dasen Lin,
  • Ahmadjan Muhammadhaji

摘要

This work examines Turing instability and pattern formation in a predator-prey system incorporating fear effects and super cross-diffusion. We first establish stability criteria for equilibrium states both with and without super cross-diffusion, demonstrating that cross-diffusion can destabilize otherwise stable equilibria. Linear stability analysis subsequently derives precise conditions for Turing instability, revealing cross-diffusion as the fundamental mechanism driving spatial pattern emergence. Using the cross-diffusion coefficient as a bifurcation parameter, we employ weakly nonlinear theory to derive amplitude equations governing excited modes near the Turing bifurcation threshold. Dynamical analysis of these equations elucidates structural transitions and stability properties across diverse Turing pattern formations. Theoretical predictions are validated through comprehensive numerical simulations.