Journal of Mathematical Chemistry

, Volume 43, Issue 2, pp 601–619 | Cite as

Analysis of a Monod–Haldene type food chain chemostat with seasonally variably pulsed input and washout

Article

In this paper, we introduce and study a model of a Monod–Haldene type food chain chemostat with seasonally variably pulsed input and washout. We investigate the subsystem with substrate and prey and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, prey and predator. Simple cycles may give way to chaos in a cascade of period-doubling bifurcations. Furthermore, bifurcation diagrams have shown that there exists complexity for the pulsed system including periodic doubling cascade, periodic halving cascade and Pitchfork bifurcations and tangent bifurcations.

Keywords

Monod–Haldene growth rate chemostat seasonally variably pulsed input and washout chaos 

AMS subject classification

34C35 92D25 

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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.College of ScienceJimei UniversityXiamenP.R. China
  2. 2.Department of Mathematics and Computer ScienceYulin Normal UniversityYulinP.R. China
  3. 3.Department of Information and Computation SciencesGuangxi University of TechnologyLiuzhouP.R. China

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