Existence and stability of traveling waves for Leslie-Gower predator-prey system with nonlocal diffusion

Hongmei Cheng; Rong Yuan

doi:10.3934/dcds.2017236

Article Contents

2017, Volume 37, Issue 10: 5433-5454. Doi: 10.3934/dcds.2017236

This issue Previous Article Topological entropy of level sets of empirical measures for non-uniformly expanding maps Next Article Constructing attracting cycles for Halley and Schröder maps of polynomials

Existence and stability of traveling waves for Leslie-Gower predator-prey system with nonlocal diffusion

Hongmei Cheng^1, , and
Rong Yuan^2,

1.
School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
2.
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

* Corresponding author: Hongmei Cheng
* Corresponding author: Hongmei Cheng

Received: June 2016

Revised: June 2017

Published: October 2017

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Abstract

This paper will mainly study the information about the existence and stability of the invasion traveling waves for the nonlocal Leslie-Gower predator-prey model. By using an invariant cone in a bounded domain with initial function being defined on and applying the Schauder's fixed point theorem, we can obtain the existence of traveling waves. Here, the compactness of the support set of dispersal kernel is needed when passing to an unbounded domain in the proof. Then we use the weighted energy to prove that the invasion traveling waves are exponentially stable as perturbation in some exponentially as $x\to-\infty $. Finally, by defining the bilateral Laplace transform, we can obtain the nonexistence of the traveling waves.

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Mathematics Subject Classification: Primary: 35B05, 35B40, 35A05; Secondary: 35R99.

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