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Pinning control of successive lag synchronization on a dynamical network with noise perturbation

Author

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  • Wang, Mengchen
  • Lu, Xiaowen
  • Yang, Qi
  • Ma, Zhongjun
  • Cheng, Jun
  • Li, Kezan

Abstract

In recent years, the successive lag synchronization (SLS) has been deeply analyzed, however, the control theory of SLS on complex networks with noise perturbation is lacking. To this end, this paper focuses on the pinning control of SLS on a dynamical network with noise perturbation. Both the constant pinning control law and adaptive pinning control law are designed respectively to push the network to achieve the desired SLS. By utilizing the Lyapunov stability theory of stochastic differential equations, several sufficient conditions for the controlled networks to achieve the SLS are obtained. The influences of network structure, noise strength and coupling strength on the realization of SLS are also discussed. We find that the noise can suppress or even destroy the realization of SLS. Meanwhile, we attain the index set of pinned nodes, which can tell us whether a node should be controlled or not. In particular, those nodes with zero in-degree must be controlled to achieve SLS, while those nodes with non-zero in-degree need not to be controlled if the coupling strength is large enough. All theoretical results are verified by numerical simulations.

Suggested Citation

  • Wang, Mengchen & Lu, Xiaowen & Yang, Qi & Ma, Zhongjun & Cheng, Jun & Li, Kezan, 2022. "Pinning control of successive lag synchronization on a dynamical network with noise perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    • Handle: RePEc:eee:phsmap:v:593:y:2022:i:c:s0378437122000292
    DOI: 10.1016/j.physa.2022.126899
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    References listed on IDEAS

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    1. Yihan Fan & Hongmei Liu & Jun Mei, 2015. "Semiglobal Finite-Time Synchronization of Complex Dynamical Networks via Periodically Intermittent Control," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-12, May.
    2. Rathinasamy Sakthivel & Ramalingam Sakthivel & Boomipalagan Kaviarasan & Chao Wang & Yong-Ki Ma, 2018. "Finite-Time Nonfragile Synchronization of Stochastic Complex Dynamical Networks with Semi-Markov Switching Outer Coupling," Complexity, Hindawi, vol. 2018, pages 1-13, January.
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    Cited by:

    1. Meng, Liang & Bao, Haibo, 2022. "Synchronization of delayed complex dynamical networks with actuator failure by event-triggered pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    2. Chen, Xiaolu & Weng, Tongfeng & Li, Chunzi & Yang, Huijie, 2022. "Synchronization of reservoir computing models via a nonlinear controller," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).

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