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Effect of delayed response in growth on the dynamics of a chemostat model with impulsive input

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  • Jiao, Jianjun
  • Yang, Xiaosong
  • Chen, Lansun
  • Cai, Shaohong

Abstract

In this paper, a chemostat model with delayed response in growth and impulsive perturbations on the substrate is considered. Using the discrete dynamical system determined by the stroboscopic map, we obtain a microorganism-extinction periodic solution, further, the globally attractive condition of the microorganism-extinction periodic solution is obtained. By the use of the theory on delay functional and impulsive differential equation, we also obtain the permanent condition of the investigated system. Our results indicate that the discrete time delay has influence to the dynamics behaviors of the investigated system, and provide tactical basis for the experimenters to control the outcome of the chemostat. Furthermore, numerical analysis is inserted to illuminate the dynamics of the system affected by the discrete time delay.

Suggested Citation

  • Jiao, Jianjun & Yang, Xiaosong & Chen, Lansun & Cai, Shaohong, 2009. "Effect of delayed response in growth on the dynamics of a chemostat model with impulsive input," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2280-2287.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:2280-2287
    DOI: 10.1016/j.chaos.2009.03.132
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    References listed on IDEAS

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    1. El-Sheikh, M.M.A. & Mahrouf, S.A.A., 2005. "Stability and bifurcation of a simple food chain in a chemostat with removal rates," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1475-1489.
    2. Fu, Guifang & Ma, Wanbiao, 2006. "Hopf bifurcations of a variable yield chemostat model with inhibitory exponential substrate uptake," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 845-850.
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    Cited by:

    1. Xie, Youxiang & Wang, Linjun & Deng, Qicheng & Wu, Zhengjia, 2017. "The dynamics of an impulsive predator–prey model with communicable disease in the prey species only," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 320-335.
    2. Tongqian Zhang & Wanbiao Ma & Xinzhu Meng, 2017. "Impulsive control of a continuous-culture and flocculation harvest chemostat model," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(16), pages 3459-3469, December.

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