Mathematical investigations of diffusive prey–predator dynamical system

This work presents the numerical investigations for the deterministic prey–predator model. It is a reaction-diffusion mathematical model for the two-prey interacting with a single predator. The predator–prey model is an important part of the ecosystem, especially for recognizing how the population collaborates in their natural surroundings. The computational numerical scheme, namely, implicit finite difference scheme is developed. The numerical solution of the underlying model is successfully gained — the positivity of the reaction-diffusion model is established. To show the feasibility of the scheme, consistency, positivity, and stability are established by applying mathematical techniques. The numerical scheme yields stable and consistent approximations that remain positive throughout the domain. Moreover, the non-negative initial conditions and homogeneous Neumann conditions are used. For various parameter values, 3D, 2D, and parametric graphs are produced. In addition, the mathematical results are verified through numerical calculations.