Effect of toxicant on the dynamics of a delayed diffusive predator-prey model

In this paper, we investigate a delayed diffusive predator-prey model affected by toxic substance. First, the boundedness and persistence property of the model are established. Then by analyzing the associated characteristic equation, we give some conditions for the existence of Hopf bifurcation, Turing bifurcation and Turing-Hopf bifurcation. Furthermore, we study Hopf bifurcation and Turing-Hopf bifurcation induced by the delay. Finally, numerical simulations are given to illustrate our theoretical results. The numerically observed characteristics accord well with the theoretically predicted results. Theoretical and numerical simulations indicate that toxic substance affect the system greatly.