Journal of Mathematical Chemistry

, Volume 51, Issue 5, pp 1231–1248 | Cite as

The asymptotic behavior of a Chemostat model with Crowley–Martin type functional response and time delays

Original Paper

Abstract

In this paper, we introduce an improved Chemostat model with Crowley–Martin type functional response and time delays. By constructing Lyapunov functionals, the global asymptotic stability of the equilibria is shown in the case of a single species. The conditions for the global asymptotical stability of the model with time delays are obtained via monotone dynamical systems in the case of two species. Our results demonstrate that the effects of predator interference may result in coexistence of two species.

Keywords

Chemostat Crowley–Martin type functional response   Lyapunov–LaSalle invariance principle Stability Time delay 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Mathematics and Computer ScienceYanan UniversityYananChina
  2. 2.Department of Applied Mathematics, School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijingChina

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