SHANDONG SCIENCE ›› 2017, Vol. 30 ›› Issue (3): 88-93.doi: 10.3976/j.issn.1002-4026.2017.03.015

• Other Research Article • Previous Articles     Next Articles

Traveling waves and spreading speed to impulsive reaction-diffusion models

SHEN Lin, ZHOU Hong-ling*   

  1. Department of Mathematics, Huanghuai University, Zhumadian 463000,China
  • Received:2017-08-03 Online:2017-06-20 Published:2017-06-20

Abstract:

In this paper, an impulsive reaction-diffusion model with fixed moments of impulses in an unbounded domain was proposed, and the existence of spreading speed and traveling wave solutions for the model were established. First, the existence and the stability of the positive constant solutions were proved in ODE system. Second, the explicit formula of spreading speed to impulsive reaction-diffusion model was given. When certain conditions were satisfied, the spreading speed was greater than zero, which was the minimum speed of the traveling wave solutions. Finally, the numerical simulation of the system was carried out with the velocity of the water flow. The results reveal that the spread and persistence dynamics of the biotic population can be realized through the control of diffusion coefficient, flow velocity, mortality and birthrate corresponding to discrete time and continuous time respectively.

Key words: traveling waves, impulsive reaction-diffusion models, spreading speed

CLC Number: 

  • O175.26