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

In this paper, the kinetics of a class delayed reaction-diffusion mussel-algae system under Neumann boundary conditions with half-saturation constant is studied. The global existence and priori bounds as well positive equilibrium are obtained. affects stability may result in Turing instability. When exceeds certain critical value, globally asymptotically stable which means that larger forces mussel population toward extinction. By analyzing distribution roots characteristic equation two delays, parameter space can be changed by steady-state bifurcation, Hopf Hopf-Hopf bifurcation or Hopf-steady state verified some numerical simulations. Among parameters, delays drive complexity dynamics.