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<p>In this paper, we investigate a Lotka–Volterra predator–prey system with diffusion and nonlinear boundary conditions. Using the Lyapunov–Schmidt reduction method, we analyze the stability and instability of positive steady states and establish conditions for Hopf bifurcation occurrence. Our analysis specifically reveals how nonlinear boundary conditions and the conversion rate influence the Hopf bifurcation dynamics.</p>

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Stability and bifurcation of a Lotka–Volterra predator–prey diffusion system with nonlinear boundary conditions

  • 期刊论文

  • 发表日期：

    2025年10月11日

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  • Kaikai Liu,
  • Shangjiang Guo

摘要

In this paper, we investigate a Lotka–Volterra predator–prey system with diffusion and nonlinear boundary conditions. Using the Lyapunov–Schmidt reduction method, we analyze the stability and instability of positive steady states and establish conditions for Hopf bifurcation occurrence. Our analysis specifically reveals how nonlinear boundary conditions and the conversion rate influence the Hopf bifurcation dynamics.