Numerical and Analytical Study for the Stochastic Spatial Dependent Prey-Predator Dynamical System

Prey and predator are the important factor of the ecosystem. Generally, it is considered that prey-predator models depends on time and it is only required nonlinear system of equations for its dynamical study. But, it is observed that such species can move from one to place to another and in such a way there is a need of nonlinear equations which also depends on spatial as well. The stochastic prey-predator system are investigated numerically and analytically. The proposed stochastic NSFD is used for numerical study; it is consistent with given system and its linear stability analysis showed that it is unconditionally stable. There are two equilibria one is predator free and second is coexistence equilibrium. These equilibria are successfully gained in the numerical case. Extended generalized Riccati equation mapping method is applied for analytical study. The obtained solutions are of the form rational, hyperbolic, and trigonometric. For the comparative study, the unique physical problems are developed and their simulations are drawn for various choices of the parameters. The graphical behavior depicts the efficacy of our study.