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<p>In this paper, the pattern dynamics of a diffusive mussel-algae model on complex network is studied, with a focus on the effect of competition among mussels. When the competition rate exceeds the critical threshold, a uniform pattern emerges, which is attributed to the globally asymptotically stable of the coexistence equilibrium proved by constructing an appropriate Lyapunov function. In contrast, when the competition rate lies within an intermediate range, Turing patterns develop as a result of Turing instability under specific conditions. By treating the diffusion rate of algae as the bifurcation parameter, we derive the explicit threshold for Turing bifurcation and analyze the stability and direction of this bifurcation through weakly nonlinear analysis and the amplitude equation. Numerical simulations on complex networks illustrate the theoretical findings, demonstrating how network topology, the initial distributions of mussels and algae and the competition rate among mussels jointly shape the spatial patterns.</p>

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Pattern dynamics of a mussel-algae model with networked diffusion: effect of competition among mussels

  • 期刊论文

  • 发表日期：

    2026年7月23日

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  • Wenzhen Gan,
  • Gongyi Jin,
  • Canrong Tian

摘要

In this paper, the pattern dynamics of a diffusive mussel-algae model on complex network is studied, with a focus on the effect of competition among mussels. When the competition rate exceeds the critical threshold, a uniform pattern emerges, which is attributed to the globally asymptotically stable of the coexistence equilibrium proved by constructing an appropriate Lyapunov function. In contrast, when the competition rate lies within an intermediate range, Turing patterns develop as a result of Turing instability under specific conditions. By treating the diffusion rate of algae as the bifurcation parameter, we derive the explicit threshold for Turing bifurcation and analyze the stability and direction of this bifurcation through weakly nonlinear analysis and the amplitude equation. Numerical simulations on complex networks illustrate the theoretical findings, demonstrating how network topology, the initial distributions of mussels and algae and the competition rate among mussels jointly shape the spatial patterns.