Traveling wave solutions of  n ‐dimensional delayed reaction–diffusion systems and application to four‐dimensional predator–prey systems | Zendy

Shang Xiaohui | Zendy; Du Zengji | Zendy; Lin Xiaojie | Zendy

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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.

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