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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

Bifurcation and Stability Analysis of a Food Web in a Chemostat

S.M. Sohel Rana1
  • 1 University of Dhaka, Bangladesh

Abstract

In this study, a classical model describing a food web in a chemostat involving three species competing for non-reproducing, growth rate-limiting nutrient in which one of the competitors predates on one of the other competitors is considered. Quantitative analyses of non-negativity and boundedness of solution trajectories, dissipativity, behavior around equilibria, global stability and persistence of the model equations are analyzed. We present the global stability of equilibria by constructing a Lyapunov function. Hopf bifurcation theory is applied.

Journal of Mathematics and Statistics
Volume 12 No. 4, 2016, 213-224

DOI: https://doi.org/10.3844/jmssp.2016.213.224

Submitted On: 17 November 2014 Published On: 22 October 2016

How to Cite: Rana, S. S. (2016). Bifurcation and Stability Analysis of a Food Web in a Chemostat. Journal of Mathematics and Statistics, 12(4), 213-224. https://doi.org/10.3844/jmssp.2016.213.224

Open AccessCopyright: © 2016 S.M. Sohel Rana. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Chemostat
  • Food Web
  • Global Stability
  • Hopf Bifurcation
  • Dissipative