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Dynamic optimal control at Hopf bifurcation of a Newman–Watts model of small-world networks via a new PD1n scheme

Author

Listed:
  • Si, Lingzhi
  • Xiao, Min
  • Wang, Zhengxin
  • Huang, Chengdai
  • Cheng, Zunsgui
  • Tao, Binbin
  • Xu, Fengyu

Abstract

In this paper, a neoteric fractional-order Proportional–Derivative (PD) feedback controller is proposed to address the problem of bifurcation control for an integer-order small-world network model with discrete delay. The time delay is selected as the bifurcation parameter, and sufficient conditions for guaranteeing the stability and generating Hopf bifurcation are constructed by analyzing the stability of the controlled system. By regulating the controller parameters, the dynamic behavior for the controlled system can be effectively optimized. Finally, by simulating numerical examples, theoretical derivations are verified and the relationships between the onset of the Hopf bifurcation and the controller parameters are obtained.

Suggested Citation

  • Si, Lingzhi & Xiao, Min & Wang, Zhengxin & Huang, Chengdai & Cheng, Zunsgui & Tao, Binbin & Xu, Fengyu, 2019. "Dynamic optimal control at Hopf bifurcation of a Newman–Watts model of small-world networks via a new PD1n scheme," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 532(C).
    • Handle: RePEc:eee:phsmap:v:532:y:2019:i:c:s0378437119310337
    DOI: 10.1016/j.physa.2019.121769
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    Citations

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    Cited by:

    1. Huang, Chengdai & Liu, Heng & Chen, Xiaoping & Zhang, Minsong & Ding, Ling & Cao, Jinde & Alsaedi, Ahmed, 2020. "Dynamic optimal control of enhancing feedback treatment for a delayed fractional order predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    2. He, Haoming & Xiao, Min & Lu, Yunxiang & Wang, Zhen & Tao, Binbin, 2023. "Control of tipping in a small-world network model via a novel dynamic delayed feedback scheme," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    3. He, Haoming & Xiao, Min & He, Jiajin & Zheng, Weixing, 2024. "Regulating spatiotemporal dynamics for a delay Gierer–Meinhardt model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).

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