Spatiotemporal dynamics for a diffusive mussel–algae model near a Hopf bifurcation point

Abstract

In this paper, the Hopf bifurcation and Turing instability for a mussel–algae model are investigated. Through analysis of the corresponding kinetic system, the existence and stability conditions of the equilibrium and the type of Hopf bifurcation are studied. Via the center manifold and Hopf bifurcation theorem, sufficient conditions for Turing instability in equilibrium and limit cycles are obtained, respectively. In addition, we find that the strip patterns are mainly induced by Turing instability in equilibrium and spot patterns are mainly induced by Turing instability in limit cycles by numerical simulations. These provide a comprehension on the complex pattern formation of a mussel–algae system.

Bifurcation analysis in a diffusion mussel-algae interaction system with delays considering the half-saturation constant

“…Their results suggested that the regular patterning in mussel beds were caused by the high mobility of algae or the low diffusion of mussels. Zhong et al [14] investigated the spatiotemporal dynamics for a diffusive mussel-algae model near a Hopf bifurcation point. They found that the strip patterns were mainly induced by Turing instability in equilibrium and spot patterns were mainly induced by Turing instability in limit cycles by numerical simulations.…”