Stability analysis of the three-dimensional environment pollution dynamical system with time delay

In this paper we consider the environment pollution dynamical system described by the ordinary differential equations. Firstly, we establish the three-dimensional environment pollution dynamical system which reflects the relationships among the air quality index, population and economic growth. Secondly, by introducing the effect of the time delay we establish the three-dimensional environment pollution dynamical system with time delay. And then we analyze the stability of the system with time delay by using the stability switch theory of the differential equations. Thirdly, we show the properties of the Hopf bifurcation. Finally, numerical simulations have been given to show the effectiveness of the main results.