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

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Keywords

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