Numerical Bifurcation Analysis to Study Periodic Traveling Wave Solutions in a Model of Young Mussel Beds

Authors

  • Md Ariful Islam Arif Department of Mathematics, Jahangirnager University, Savar, Dhaka-1342
  • M Osman Gani Department of Mathematics, Jahangirnager University, Savar, Dhaka-1342

DOI:

https://doi.org/10.3329/ganit.v38i0.39781

Keywords:

Essential spectrum, Hopfbifurcation, Eckhaus bifurcation, mussel beds, periodic traveling wave, reaction-diffusion-advection

Abstract

Self-bottomed mussel beds are dominant feature of ecosystem-scale self-organization. Regular spatial patterns of mussel beds in inter-tidal zone are typical, aligned perpendicular to the average incoming tidal flow. In this paper, we consider a two-variable partial differential equations model of young mussel beds. Our aim is to study the existence and stability of periodic traveling waves in a one-parameter family of solutions. We consider a parameter regime to show pattern existence in the model of young mussel beds. In addition, it is found that the periodic traveling waves changes their stability by two ways: Hopf type and Eckhaus type. We explain this stability by the calculation of essential spectra at different grid points in the two-dimensional parameter plane.

GANIT J. Bangladesh Math. Soc.Vol. 38 (2018) 1-10

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Author Biographies

Md Ariful Islam Arif, Department of Mathematics, Jahangirnager University, Savar, Dhaka-1342

Department of Mathematics

M Osman Gani, Department of Mathematics, Jahangirnager University, Savar, Dhaka-1342

Department of Mathematics

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Published

2018-12-30

How to Cite

Arif, M. A. I., & Gani, M. O. (2018). Numerical Bifurcation Analysis to Study Periodic Traveling Wave Solutions in a Model of Young Mussel Beds. GANIT: Journal of Bangladesh Mathematical Society, 38, 1–10. https://doi.org/10.3329/ganit.v38i0.39781

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Articles