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Stabilization for Stochastic Coupled Kuramoto Oscillators via Nonlinear Distributed Feedback Control

Author

Listed:
  • Rui Kang

    (Department of Mathematics, Northeast Forestry University, Harbin 150040, China)

  • Shang Gao

    (Department of Mathematics, Northeast Forestry University, Harbin 150040, China)

Abstract

This paper investigates the stabilization for stochastic coupled Kuramoto oscillators (SCKOs) via nonlinear distributed feedback control. An original nonlinear distributed feedback control with the advantages of fast response, no steady-state deviation, and easy implementation is designed to stabilize SCKOs. With the help of the Lyapunov method and stochastic analysis skills, some novel sufficient conditions guaranteeing the stochastic stability for SCKOs are provided by constructing a new and suitable Lyapunov function for SCKOs. Finally, a numerical example is given to illustrate the effectiveness and applicability of the theoretical result.

Suggested Citation

  • Rui Kang & Shang Gao, 2022. "Stabilization for Stochastic Coupled Kuramoto Oscillators via Nonlinear Distributed Feedback Control," Mathematics, MDPI, vol. 10(18), pages 1-9, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3329-:d:914653
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    References listed on IDEAS

    as
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    4. Gao, Shang & Guo, Haihua & Chen, Tianrui, 2019. "The existence of periodic solutions for discrete-time coupled systems on networks with time-varying delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    5. Guo, Ying & Zhao, Wei & Ding, Xiaohua, 2019. "Input-to-state stability for stochastic multi-group models with multi-dispersal and time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 114-127.
    6. Gao, Shang & Wu, Boying, 2015. "On input-to-state stability for stochastic coupled control systems on networks," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 90-101.
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