Competitive Reaction-diffusion Systems: Travelling Waves and Numerical Solutions

Main Article Content

Md. Kamrujjaman
Asif Ahmed
Shohel Ahmed

Abstract

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).

Keywords:
Nonlinear PDEs, travelling wave solutions, reaction-diffusion, Crank-Nicolson scheme.

Article Details

How to Cite
Kamrujjaman, M., Ahmed, A., & Ahmed, S. (2019). Competitive Reaction-diffusion Systems: Travelling Waves and Numerical Solutions. Advances in Research, 19(6), 1-12. https://doi.org/10.9734/air/2019/v19i630140
Section
Original Research Article

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