Stability and Hopf bifurcation of a diffusive plankton model with time-delay and mixed nonlinear functional responses

Abstract

In this paper, we deal with a plankton reaction–diffusion model with time-delay and two different functional responses. Firstly, we consider the global stability of boundary equilibrium point. Secondly, we investigate the existence, uniqueness and stability of internal equilibrium point without time-delay. Then, we analyze the existence of Hopf bifurcation emitting from internal equilibrium point and give some characteristics on Hopf branch in detail. A new finding is presented, specifically, we find that there exist two critical values which have important effects on the occurrence of Hopf bifurcation. Finally, a few numerical examples are presented to check and illustrate the theoretical analysis, some simulation graphs, including the spatiotemporal graphs, trajectory graphs and phase portraits are depicted graphically.