Bifurcation and Stability of a Spatiotemporal Prey–Predator Model: A Computational Perspective

Abstract

In this research work, a ratio-dependent prey–predator system is investigated for bifurcation and stability analysis. The unique existence of the solution, boundedness, and positivity of the temporal model is derived. Stability analysis of positive steady states is analyzed. Stable and unstable regions for both equilibria are drawn in different parametric spaces. The parametric plots for the different initial conditions are drawn. The diffusive prey–predator model is analyzed for the bifurcation and stability regions. It is observed that the stability regions under the effect of diffusion are increased. To gain the numerical solution of the spatially extended prey–predator model, the operator splitting scheme is derived. The scheme preserves the positivity and other important features of the continuous model. Lastly, a test problem is considered to visualize the accuracy of our scheme. To show the physical behavior of the scheme, 3D and 2D plots are drawn, which clearly show the dynamics of the scheme. Theoretical results are supported by simulations.