Bifurcation and Turing instability for a freshwater tussock sedge model with nonlocal interaction

The Hopf bifurcation, Turing instability and steady state bifurcation to a fresh-water tussock sedge model with nonlocal interaction under Neumman boundary condition are investigated in this paper. First, we analyze the existence of constant steady states and the effect of the nonlocal term on the its stability and the existence of Hopf bifurcation. Furthermore, the occurrence conditions of Turing instability to such system are studied. Second, we focus on steady state bifurcation to the reaction–diffusion system with nonlocal interaction via Lyapunov–Schmidt reduced method. Finally, numerical simulations have been illustrated to verify our theoretical analysis.