Delay‐included Turing‐Hopf bifurcation in the diffusive mussel‐algae model

Abstract

In this paper, the main content is the consideration of the dynamics of a diffusive mussel‐algae model with delay subject to Neumann boundary condition. We will analyze the corresponding characteristic equation and study the existence of delay‐induced Hopf bifurcation and steady state bifurcation. What's more, according to the results of Song et al. we calculated the normal form on the center mainfold and obtained the formulae of the delay‐induced Turing‐Hopf bifurcation, and we also investigate the dynamical behaviors near the Turing‐Hopf bifurcation point. Finally, in order to illustrate and extend our theoretical results, some exact numerical simulations are given out as the authentication.