In this talk, we work on a model of the prey-predator system to see the effect of system components on species distribution for both temporal and spatial structure. In some cases, changing environmental conditions results in extinction or leads the survival of species. So in this work, the prey-predator system is studied numerically to detail the species sustainability with the assist of gradient addition on systems` parameter. The model consists of two coupled diffusion equations. Extensive numerical simulations on ODE (Ordinary differential equation) and PDE (Partial Differential Equations) are investigated to understand the underlying structure of system response for changing surrounding environmental conditions effect with the assist of system parameters. Obtained results show that the sustainability of species depends on the choice of parameters  

Keywords - Prey-predator system; temporal distribution; spatial distribution; mathematical modelling; simulation

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