Abstract: By using the stability and bifurcation theory of differential equation, we studied the dynamic properties of a class of reaction-diffusion models for plankton with a non-local competition. Firstly, we gave the conditions for the existence and stability of positive constant equilibrium solutions. Secondly, we gave the conditions for the occurrence of Hopf bifurcation and steady-state bifurcation at the positive constant equilibrium solution, and calculated the properties of these bifurcations. Finally, we explained the  theoretical analysis results through numerical simulation.

Key words: plankton model, non-local competition, Hopf bifurcation, steady-state bifurcation, diffusion