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Traveling wave solutions of n ‐dimensional delayed reaction–diffusion systems and application to four‐dimensional predator–prey systems
Author(s) -
Shang Xiaohui,
Du Zengji,
Lin Xiaojie
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3595
Subject(s) - traveling wave , mathematics , reaction–diffusion system , diffusion , fixed point theorem , mathematical analysis , comparison theorem , schauder fixed point theorem , predation , physics , picard–lindelöf theorem , biology , thermodynamics , paleontology
This paper deals with the existence of traveling wave solutions for n ‐dimensional delayed reaction–diffusion systems. By using Schauder's fixed point theorem, we establish the existence result of a traveling wave solution connecting two steady states by constructing a pair of upper–lower solutions that are easy to construct. As an application, we apply our main results to a four‐dimensional delayed predator–prey system and obtain the existence of traveling wave solutions. Copyright © 2016 John Wiley & Sons, Ltd.