Global dynamics of competition models with nonsymmetric nonlocal dispersals when one diffusion rate is small

Xueli Bai; Fang Li

doi:10.3934/dcds.2020035

Article Contents

2020, Volume 40, Issue 6: 3075-3092. Doi: 10.3934/dcds.2020035 open access

This issue Previous Article Evolution equations involving nonlinear truncated Laplacian operators Next Article Mean field equations on tori: Existence and uniqueness of evenly symmetric blow-up solutions

Global dynamics of competition models with nonsymmetric nonlocal dispersals when one diffusion rate is small

Xueli Bai^1, and
Fang Li^2, ,

1.
Department of Applied Mathematics, Northwestern Polytechnical University, 127 Youyi Road(West), Beilin 710072, Xi'an, China
2.
School of Mathematics, Sun Yat-sen University, No. 135, Xingang Xi Road, Guangzhou 510275, China

^* Corresponding author: Fang Li
^* Corresponding author: Fang Li

Received: January 31, 2019

Revised: March 31, 2019

Published: March 2020

The first author is supported by Shaanxi NSF (No. S2017-ZRJJ-MS-0104), Special financial aid to post-doctor research fellow (No. 2017T100768), Shaanxi Postdoctoral Science Foundation (2017BSHTDZZ16) and Alexander von Humboldt Foundation. The second author is supported by NSF of China (No. 11431005, 11971498) and the Fundamental Research Funds for the Central Universities

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Abstract

In this paper, we study the global dynamics of a general $ 2\times 2 $ competition models with nonsymmetric nonlocal dispersal operators. Our results indicate that local stability implies global stability provided that one of the diffusion rates is sufficiently small. This paper extends the work in [3], where Lotka-Volterra competition models with symmetric nonlocal operators are considered, to more general competition models with nonsymmetric operators.

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Mathematics Subject Classification: Primary: 45G15, 45M05; Secondary: 45M10, 45M20.

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