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In this paper, we consider a competitive reaction-diffusion model to describe the existence of travelling wave solutions of two competing species. Moreover, the non-linear system is also studied by introducing different competitive-cooperative coefficients; constant and spatially distributed which leads to the persistence and extinction of organisms in a heterogeneous environment of population biology. If the diffusion coefficients and other parameters are positive constant, it is seen that one species is in extinction by the other and coexistence is also possible under certain conditions on carrying capacity. The results are numerically investigated by using the Finite difference method (FDM).
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