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Complex dynamics and impulsive control of a chemostat model under the ratio threshold policy

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  • Li, Wenjie
  • Ji, Jinchen
  • Huang, Lihong
  • Zhang, Ying

Abstract

In this paper, we study the periodic solution and global stability of a chemostat model under impulsive control. First, we investigate the positivity and boundedness of the solution of the controlled system. Second, we find the periodic solution of the controlled system by employing the Poincare map and Brouwer’s fixed-point theorem. Furthermore, we obtain a sufficient condition which allows the existence of orbitally stable order-k periodic solutions (k=1,2) by using the comparison method and the vector field analysis. We find that the controlled system exists a unique positive equilibrium point that is globally asymptotically stable (GAS) under some conditions. Finally, we provide two numerical examples to verify the correctness of the theoretical results.

Suggested Citation

  • Li, Wenjie & Ji, Jinchen & Huang, Lihong & Zhang, Ying, 2023. "Complex dynamics and impulsive control of a chemostat model under the ratio threshold policy," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922012565
    DOI: 10.1016/j.chaos.2022.113077
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    References listed on IDEAS

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    1. Yu, Shuxian & Zhou, Jie & Guan, Shuguang, 2022. "The structure of uni-directional chain for the synchronization of networked chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Li, Wenjie & Zhang, Ying & Huang, Lihong, 2023. "Dynamics analysis of a predator–prey model with nonmonotonic functional response and impulsive control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 529-555.
    3. Jiang, Guirong & Lu, Qishao & Qian, Linning, 2007. "Complex dynamics of a Holling type II prey–predator system with state feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 448-461.
    4. Liu, Qiong & Zhang, Meng & Chen, Lansun, 2019. "State feedback impulsive therapy to SIS model of animal infectious diseases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 222-232.
    5. Xie, Yingkang & Wang, Zhen, 2022. "A ratio-dependent impulsive control of an SIQS epidemic model with non-linear incidence," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    6. Zhang, Meng & Zhao, Yi & Chen, Lansun & Li, Zeyu, 2020. "State feedback impulsive modeling and dynamic analysis of ecological balance in aquaculture water with nutritional utilization rate," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    7. Fengmei Tao & Zhong Zhao & Lansun Chen, 2018. "Chemostat Model of Competition between Plasmid-Bearing and Plasmid-Free Organism with the Impulsive State Feedback Control," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-10, October.
    8. Li, Wenjie & Huang, Lihong & Guo, Zhenyuan & Ji, Jinchen, 2020. "Global dynamic behavior of a plant disease model with ratio dependent impulsive control strategy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 120-139.
    9. Wu, Dayu & Liu, Ying & Tang, Ming & Xu, Xiao-Ke & Guan, Shuguang, 2022. "Impact of hopping characteristics of inter-layer commuters on epidemic spreading in multilayer networks," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    10. Yang, Jin & Tang, Guangyao, 2019. "Piecewise chemostat model with control strategy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 126-142.
    11. Wang, Xiaoyan & Han, Xiujing & Chen, Zhangyao & Bi, Qinsheng & Guan, Shuguang & Zou, Yong, 2022. "Multi-scale transition network approaches for nonlinear time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    12. Yajie Li & Xinzhu Meng, 2019. "Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment," Discrete Dynamics in Nature and Society, Hindawi, vol. 2019, pages 1-15, February.
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    1. Li, Wenjie & Zhang, Ying & Cao, Jinde & Wang, Dongshu, 2023. "Large time behavior in a reaction diffusion epidemic model with logistic source," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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