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.

Automated summary

In this paper, we investigate a delayed diffusive predator-prey model affected by toxic substance. We establish the boundedness and persistence property of the model and analyze the conditions for the existence of Hopf bifurcation, Turing bifurcation and Turing-Hopf bifurcation by analyzing the associated characteristic equation. Further, we study the effects of delay on Hopf bifurcation and Turing-Hopf bifurcation. Numerical simulations confirm the theoretical results and indicate that toxic substance greatly affects the system.