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

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