A Leslie-Gower predator-prey model with a free boundary

Yunfeng Liu; Zhiming Guo; Mohammad El Smaily; Lin Wang

doi:10.3934/dcdss.2019133

Article Contents

2019, Volume 12, Issue 7: 2063-2084. Doi: 10.3934/dcdss.2019133

This issue Previous Article Solutions of nonlinear periodic Dirac equations with periodic potentials Next Article Periodic and subharmonic solutions for a 2$n$th-order $\phi_c$-Laplacian difference equation containing both advances and retardations

A Leslie-Gower predator-prey model with a free boundary

a.
School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
b.
Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, Canada

* Corresponding author: Zhiming Guo, guozm@gzhu.edu.cn
* Corresponding author: Zhiming Guo, guozm@gzhu.edu.cn

Dedicated to Professor Norman Dancer on the occasion of his 70th birthday

Received: December 2017

Revised: June 2018

Published: June 2019

The work of ME and LW was supported by NSERC Discovery Grants from the Natural Sciences and Engineering Research Council of Canada (NSERC). YL and ZG acknowledge support from the National Natural Science Foundation of China (No.11771104), Program for Changjiang Scholars and Innovative Research Team in University (IRT-16R16).YL was supported by the Innovation Research for the Postgraduates of Guangzhou University under Grant No.2017GDJC-D05.

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Abstract

In this paper, we consider a Leslie-Gower predator-prey model in one-dimensional environment. We study the asymptotic behavior of two species evolving in a domain with a free boundary. Sufficient conditions for spreading success and spreading failure are obtained. We also derive sharp criteria for spreading and vanishing of the two species. Finally, when spreading is successful, we show that the spreading speed is between the minimal speed of traveling wavefront solutions for the predator-prey model on the whole real line (without a free boundary) and an elliptic problem that follows from the original model.

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Mathematics Subject Classification: Primary: 35K57, 35R35, 92C50, 92B99.

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