The time dependent non-linear reaction-diffusion equation in predator–prey models in Lotka- Volterra system has been formulated and solved analytically and numerically. Analytical expressions for the prey and predator populations are derived by using the HPM. The primary result of this work is simple approximate calculations of prey and predator populations for all values of dimensionless parameter ∝ and the constant value l and m . The HPM is an extremely simple method and it is also a promising method to solve other non-linear equations. This method can be easily extended to find the solution of all other non-linear equations.
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