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Dynamical analysis of a five-dimensioned chemostat model with impulsive diffusion and pulse input environmental toxicant

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  • Jiao, Jianjun
  • Ye, Kaili
  • Chen, Lansun

Abstract

In this paper, we consider a five-dimensioned chemostat model with impulsive diffusion and pulse input environmental toxicant. Using the discrete dynamical system determined by the stroboscopic map, we obtain a microorganism-extinction periodic solution. Further, it is globally asymptotically stable. The permanent condition of the investigated system is also analyzed by the theory on impulsive differential equation. Our results reveal that the chemostat environmental changes play an important role on the outcome of the chemostat.

Suggested Citation

  • Jiao, Jianjun & Ye, Kaili & Chen, Lansun, 2011. "Dynamical analysis of a five-dimensioned chemostat model with impulsive diffusion and pulse input environmental toxicant," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 17-27.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:1:p:17-27
    DOI: 10.1016/j.chaos.2010.11.001
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    Cited by:

    1. Liu, Meng & Wang, Ke, 2012. "Persistence and extinction of a single-species population system in a polluted environment with random perturbations and impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1541-1550.
    2. Mengnan Chi & Wencai Zhao, 2019. "Dynamical Analysis of Two-Microorganism and Single Nutrient Stochastic Chemostat Model with Monod-Haldane Response Function," Complexity, Hindawi, vol. 2019, pages 1-13, March.
    3. Zhao, Zhong & Wu, Xianbin, 2014. "Nonlinear analysis of a delayed stage-structured predator–prey model with impulsive effect and environment pollution," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1262-1268.
    4. Zhao, Zhong & Li, Qiuying & Chen, Lansun, 2018. "Effect of rhizosphere dispersal and impulsive input on the growth of wetland plant," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 152(C), pages 69-80.
    5. Liu, Qun & Chen, Qingmei, 2015. "Dynamics of stochastic delay Lotka–Volterra systems with impulsive toxicant input and Lévy noise in polluted environments," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 52-67.

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