Confidence domain in the stochastic competition chemostat model with feedback control

  • Chao-qun Xu
  • San-ling YuanEmail author
  • Tong-hua Zhang


This paper studies a stochastically forced chemostat model with feedback control in which two organisms compete for a single growth-limiting substrate. In the deterministic counterpart, previous researches show that the coexistence of two competing organisms may be achieved as a stable positive equilibrium or a stable positive periodic solution by different feedback schedules. In the stochastic case, based on the stochastic sensitivity function technique, we construct the confidence domains for different feedback schedules which allow us to find the configurational arrangements of the stochastic attractors and analyze the dispersion of the random states of the stochastic model.


stochastic chemostat model feedback control white noise confidence domain 

MR Subject Classification

34K50 60H10 92B05 


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Copyright information

© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of ScienceJiangsu UniversityZhenjiang, JiangsuChina
  2. 2.College of ScienceUniversity of Shanghai for Science and TechnologyShanghaiChina
  3. 3.Department of MathematicsSwinburne University of TechnologyHawthorn, VIC.Australia

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