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<p>The aim of this work is to investigate a predator–prey model through a multi-step approach. Firstly, we propose a model incorporating a Holling type-II interaction function with diffusive effects. Secondly, we determine the stability conditions near equilibrium points using Hopf bifurcation analysis and then introduce Lyapunov function and obtain global stability near equilibrium. Thirdly, we apply traveling wave analysis and geometric perturbation theory to obtain approximate solutions near these equilibrium points. Fourthly, we examine the stability of solutions near steady-state solutions. Fifthly, we obtain the solution by using the theory of self-similar structures. Finally we obtain the non-stationary solutions by using nonlinear point scaling, providing a comprehensive understanding of the model’s dynamics.</p>

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Analysis of Solutions for Modified Leslie-Gower Model with Fear Effect and Diffusion

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年12月6日

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  • Saqib Zia,
  • Saeed ur Rahman,
  • Amna Waqar,
  • Wei Sin Koh

摘要

The aim of this work is to investigate a predator–prey model through a multi-step approach. Firstly, we propose a model incorporating a Holling type-II interaction function with diffusive effects. Secondly, we determine the stability conditions near equilibrium points using Hopf bifurcation analysis and then introduce Lyapunov function and obtain global stability near equilibrium. Thirdly, we apply traveling wave analysis and geometric perturbation theory to obtain approximate solutions near these equilibrium points. Fourthly, we examine the stability of solutions near steady-state solutions. Fifthly, we obtain the solution by using the theory of self-similar structures. Finally we obtain the non-stationary solutions by using nonlinear point scaling, providing a comprehensive understanding of the model’s dynamics.