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Control of tipping in a small-world network model via a novel dynamic delayed feedback scheme

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Listed:
  • He, Haoming
  • Xiao, Min
  • Lu, Yunxiang
  • Wang, Zhen
  • Tao, Binbin

Abstract

Small-world networks have been of increasing interest because of their high similarity with complex networks in reality. Achievements about controlling the propagation and evolution of small world networks have been highlighted, but little is known about the tipping mechanism and control of such network. In this paper, a novel dynamic delayed feedback scheme is put forward and applied to successfully control the tipping phenomenon in small-world networks. Firstly, the linear characteristic equation of the controlled system is analyzed and the conditions for stability and the occurrence of bifurcation-induced tipping are given. Then, the direction of Hopf bifurcation, which reveals the further evolution mechanism of tipping, is analyzed by using the normal form theory and center manifold reduction. Finally, the numerical simulations are provided to support the theoretical analysis and to verify the effectiveness of the proposed dynamic delayed feedback controller for the small-world network.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923000723
    DOI: 10.1016/j.chaos.2023.113171
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    References listed on IDEAS

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    1. M. E. J. Newman & D. J. Watts, 1999. "Renormalization Group Analysis of the Small-World Network Model," Working Papers 99-04-029, Santa Fe Institute.
    2. Erkaymaz, Okan & Ozer, Mahmut, 2016. "Impact of small-world network topology on the conventional artificial neural network for the diagnosis of diabetes," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 178-185.
    3. Zhou, Weigang & Huang, Chengdai & Xiao, Min & Cao, Jinde, 2019. "Hybrid tactics for bifurcation control in a fractional-order delayed predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 183-191.
    4. Guan, Xueyi & Cheng, Rongjun & Ge, Hongxia, 2021. "Bifurcation control of optimal velocity model through anticipated effect and response time-delay feedback methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    5. 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).
    6. Huang, Chengdai & Li, Huan & Cao, Jinde, 2019. "A novel strategy of bifurcation control for a delayed fractional predator–prey model," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 808-838.
    7. Akhtar, S. & Ahmed, R. & Batool, M. & Shah, Nehad Ali & Chung, Jae Dong, 2021. "Stability, bifurcation and chaos control of a discretized Leslie prey-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    8. Zheng, Yi & Wu, Xiaoqun & Fan, Ziye & Wang, Wei, 2022. "Identifying topology and system parameters of fractional-order complex dynamical networks," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    9. He, Jia & Xue, Yumei, 2018. "Scale-free and small-world properties of hollow cube networks," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 11-15.
    10. Mishra, Ankit & Bandyopadhyay, Jayendra N. & Jalan, Sarika, 2021. "Multifractal analysis of eigenvectors of small-world networks," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
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