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Discrete Dynamics in Nature and Society
Volume 2018, Article ID 4873803, 8 pages
https://doi.org/10.1155/2018/4873803
Research Article

Minimal Wave Speed in a Predator-Prey System with Distributed Time Delay

Department of Basic, Zhejiang University of Water Resources and Electric Power, Hangzhou, Zhejiang 310018, China

Correspondence should be addressed to Fuzhen Wu; ten.haey@uwhzuf

Received 14 March 2018; Accepted 6 May 2018; Published 31 May 2018

Academic Editor: Nikos I. Karachalios

Copyright © 2018 Fuzhen Wu and Dongfeng Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with the minimal wave speed of traveling wave solutions in a predator-prey system with distributed time delay, which does not satisfy comparison principle due to delayed intraspecific terms. By constructing upper and lower solutions, we obtain the existence of traveling wave solutions when the wave speed is the minimal wave speed. Our results complete the known conclusions and show the precisely asymptotic behavior of traveling wave solutions.