Dynamic behavior analysis of a diffusive plankton model with defensive and offensive effects.

• A diffusive plankton model with defensive and offensive effects is considered. • Hopf bifurcations of plankton model without and with diffusion are studied. • Turing instability of diffusive model is analyzed. • The impacts of defense and offense on the coexistence of plankton are discussed. This paper investigates the dynamic behavior of a diffusive plankton model with defensive and offensive effects in two cases. For the single compartment model, we first derive the sufficient conditions for the stability and Hopf bifurcation of coexisting equilibrium, which implies that the changes of defense and offense can cause oscillation of planktonic population. Then the properties of Hopf bifurcation are discussed by center manifold theorem. For the spatially extended model, we obtain the sufficient conditions for Turing instability and Hopf bifurcation. It is observed that spatial patterns put in place, under the interaction of diffusion, defense and offense. Finally, some numerical simulations are carried out to support the analytical results. [ABSTRACT FROM AUTHOR]