Validating Numerical to Theoretical Solutions in a Reaction-Diffusion with Linear Cross-Diffusion Systems.

  • Hussaini Salihu Ndakwo Nasarawa state university Keffi Nigeria
  • Umar Mallam Abdulkarim Department of Mathematics, Nasarawa State University, PMB 1022 Keffi. Nigeria
  • Bello Muhammad Sulayman Department of Mathematics, Nasarawa State University, PMB 1022 Keffi. Nigeria
Keywords: Cross-diffusion driven instability, parameter space, spatial paterns, pattern formation, validation, numerical simulation, Turing theory, Finite difference method.

Abstract

In this paper, we consider a reaction diffusion system with linear cross-diffusion. We carry out the analytical study in detail and find out that, when the diffusion coefficient is unity, Turing instability does not occur, but with the introduction of cross-diffusion, the system exhibit Turing instability. The numerical results reveal that, on increasing the value of gamma, there is an occurrence of spatial patterns which conforms with the theoretical results.

The cross-diffusion coefficients really plays a vital role on the parameter spaces and spatial patterns of our system.

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References

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Published
2020-07-05
How to Cite
Ndakwo, H., Abdulkarim, U., & Sulayman, B. (2020). Validating Numerical to Theoretical Solutions in a Reaction-Diffusion with Linear Cross-Diffusion Systems. Journal of Progressive Research in Mathematics, 16(3), 2986-3000. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1874
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