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Asymptotic behavior of a stochastic ratio-dependent chemostat model#br#

DONG Qing-lai   

  1. School of Mathematics and Computer Science, Yan’an University, Yan’an 716000, Shanxi, China
  • Received:2013-11-21 Online:2014-03-20 Published:2014-05-29

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Abstract: This paper studies the asymptotic behavior of a stochastic Chemostat model with ratio-dependent functional response in which the dilution rate was influenced by white noise. The long time behavior of the model is studied. There exists a unique positive solution by stochastic comparison theorem. Using Lyapunov function, we show the washout equilibrium is stochastically asymptotically stable in the large. Furthermore, we show how the solution spirals around the positive equilibrium of deterministic system.

Key words: ratio-dependent functional response, Lyapunov function, It formula, stability, chemostat

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