Journal of Dynamics and Differential Equations

, Volume 31, Issue 4, pp 2305–2338 | Cite as

Uniqueness and Stability of Coexistence States in Two Species Models With/Without Chemotaxis on Bounded Heterogeneous Environments

  • Tahir Bachar IssaEmail author
  • Wenxian Shen


The current paper is concerned with the asymptotic dynamics of two species competition systems with/without chemotaxis in heterogeneous media. In the previous work (Issa and Shen in Persistence, coexistence and extinction in two species chemotaxis models on bounded heterogeneous environments, 2017., we find conditions on the parameters in such systems for the persistence of the two species and the existence of positive coexistence states. In this paper, we find conditions on the parameters for the uniqueness and stability of positive coexistence states of such systems. The established results are new even for the two species competition systems without chemotaxis but with space dependent coefficients.


Ultimates bounds of solutions Asymptotic stability and uniqueness of coexistence states 

Mathematics Subject Classification

35B40 35B41 37J25 92C17 



The authors also would like to thank the referee for valuable comments and suggestions which improved the presentation of this paper considerably.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsAuburn UniversityAuburnUSA

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