Influence of toxic substances on dynamical behavior of a delayed diffusive predator-prey model

In this paper, we propose and investigate a delayed diffusive predator-prey model affected by toxic substances. We first study the boundedness and persistence property of the model. By analyzing the associated characteristic equation, we obtain the conditions for the existence of steady state bifurcation, Hopf bifurcation and Turing bifurcation. Furthermore, we also study the Hopf bifurcation induced by the delay. Finally, our theoretical results are verified by numerical simulation. The numerical observation results are in good agreement with the theoretically predicted results. Theoretical and numerical simulations indicate that toxic substances have a great impact on the dynamics of the system.

Automated summary

In this paper, we investigate a delayed diffusive predator-prey model affected by toxic substances. The boundedness and persistence property of the model are studied first. Conditions for the existence of steady state bifurcation, Hopf bifurcation, and Turing bifurcation are obtained by analyzing the characteristic equation. Moreover, the Hopf bifurcation induced by the delay is also studied. Theoretical results are verified by numerical simulation, showing the significant impact of toxic substances on the system dynamics.