Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

Competitive systems with migration and the Poincaré-Bendixson theorem for a 4-dimensional case


Authors: Jifa Jiang and Xing Liang
Journal: Quart. Appl. Math. 64 (2006), 483-498
MSC (2000): Primary 34C12, 37N25; Secondary 92D40
DOI: https://doi.org/10.1090/S0033-569X-06-01016-0
Published electronically: June 14, 2006
MathSciNet review: 2259050
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, dynamics of the $ n$-species competitive system with migration is studied. It is proved that if the Jacobian matrix of the system is irreducible at every point in Int $ \mathbb{R}^{2n}_+$, then there is a defined countable family of invariant $ (2n-1)$-cells which attract all nonconvergent persistent trajectories. Moreover, it is proved that the Poincaré-Bendixson theorem holds for $ 2$-species competitive systems with migration.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 34C12, 37N25, 92D40

Retrieve articles in all journals with MSC (2000): 34C12, 37N25, 92D40


Additional Information

Jifa Jiang
Affiliation: Department of Applied Mathematics, Tongji University, Shanghai 200092, People’s Republic of China
Email: jiangjf@mail.tongji.edu.cn

Xing Liang
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
Email: xliang@ustc.edu.cn

DOI: https://doi.org/10.1090/S0033-569X-06-01016-0
Keywords: Competitive systems with migration, Poincar\'{e}-Bendixson theorem
Received by editor(s): October 19, 2005
Published electronically: June 14, 2006
Additional Notes: Research of the first author supported by the National Natural Science Foundation of China.
Research of the second author supported by the National Natural Science Foundation of China grant 10401032.
Article copyright: © Copyright 2006 Brown University


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website