Asymptotical Wave Speed and Monotone Property of Traveling Wave Solution for a Two-Species Ratio-Dependent Predator-Prey System with Free Diffusion and Discrete Delay
Zhihao Ge *
Institute of Applied Mathematics, Henan University, Kaifeng 475001, P.R. China and School of Mathematics and Information Sciences,Henan University, Kaifeng475001, P.R. China.
Qingjie Hu
School of Mathematics and Information Sciences,Henan University, Kaifeng475001, P.R. China.
Suna Ma
School of Mathematics and Information Sciences,Henan University, Kaifeng475001, P.R. China.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we consider a two-species ratio-dependent predator-prey system with free diffusion and discrete time delay. We study the asymptotical wave speed to give the necessary condition on the front speed, and prove that the traveling wave solution by combining the approach introduced by Canosa with the method of upper and lower solutions is monotone. Finally, we give a conclusion to summarize the achievements of the work.
Keywords: Asymptotical wave speed, delay, upper and lower solutions, traveling wave solution