Author(s)

Hairu Chen, Yuanfu Shao^*

College of Science, Guilin University of Technology, Guilin, China.

In this paper, we consider an impulsive competitive system with infinite delay and diffusion. Firstly, on basis of inequality estimation techniques and comparison theorem of impulsive differential equations, we obtain some sufficient conditions for the permanence and extinction of the system. Then, we establish sufficient conditions for the globally attractive of the system by constructing appropriate Lyapunov function. Besides, under different impulsive conditions, we discuss the effect of time delay and diffusion on dynamic behavior of the competitive system.

Diffusion, Infinite Delay, Permanence, Extinction, Attractive

Chen, H. and Shao, Y. (2018) The Dynamics of an Impulsive Competitive System with Infinite Delay and Diffusion. Journal of Applied Mathematics and Physics, 6, 1388-1407. doi: 10.4236/jamp.2018.66116.