Dynamics of a diffusive delayed competition and cooperation system-Reference-Cited by-同舟云学术

Dynamics of a diffusive delayed competition and cooperation system

Published:2020-01-01 Issue:1 Volume:18 Page:1230-1249
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Wei Zhangzhi¹,Zhang Xin²

Affiliation:

1. School of Mathematics and Statistics, Suzhou University , Suzhou , 234000 , China

2. School of Applied Mathematics, Nanjing University of Finance & Economics , Nanjing , 210023 , China

Abstract

Abstract In this manuscript, we first consider the diffusive competition and cooperation system subject to Neumann boundary conditions without delay terms and get the conclusion that the unique positive constant equilibrium is locally asymptotically stable. Then, we study the diffusive delayed competition and cooperation system subject to Neumann boundary conditions, and the existence of Hopf bifurcation at the positive equilibrium is obtained by regarding delay term as the parameter. By the theory of center manifold and normal form, an algorithm for determining the direction and stability of Hopf bifurcation is derived. Finally, some numerical simulations and summarizations are carried out for illustrating the theoretical analytic results.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2020-0064/pdf

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