# American Institute of Mathematical Sciences

June  2020, 40(6): 3075-3092. doi: 10.3934/dcds.2020035

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

 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

Received  February 2019 Revised  April 2019 Published  October 2019

Fund Project: 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

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.

Citation: Xueli Bai, Fang Li. Global dynamics of competition models with nonsymmetric nonlocal dispersals when one diffusion rate is small. Discrete & Continuous Dynamical Systems, 2020, 40 (6) : 3075-3092. doi: 10.3934/dcds.2020035
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