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

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.