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Stabilization of complex-valued stochastic functional differential systems on networks via impulsive control

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  • Wang, Pengfei
  • Li, Shaoyu
  • Su, Huan

Abstract

In this paper, we consider the stabilization problem of complex-valued stochastic functional differential systems on networks (CSFDNs) via impulsive control. By the aid of complex version Itô’s formula, the CSFDNs is studied in complex domain directly without splitting their real and imaginary parts. Then by combining Lyapunov-Razumikhin method and graph-theoretical technique, we give several novel stability criteria for CSFDNs. These criteria show that the impulses and connectivity of CSFDNs play important roles in the stability analysis of CSFDNs. Subsequently, the stability of complex-valued stochastic networks with time-varying delay is investigated. Finally, an illustrative example of complex-valued stochastic neural networks is presented to show the validness of the main results.

Suggested Citation

  • Wang, Pengfei & Li, Shaoyu & Su, Huan, 2020. "Stabilization of complex-valued stochastic functional differential systems on networks via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    • Handle: RePEc:eee:chsofr:v:133:y:2020:i:c:s0960077919305181
    DOI: 10.1016/j.chaos.2019.109561
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    References listed on IDEAS

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    1. Dan Liu & Song Zhu & Wenting Chang, 2017. "Mean square exponential input-to-state stability of stochastic memristive complex-valued neural networks with time varying delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(9), pages 1966-1977, July.
    2. Zhang, Lan & Yang, Xinsong & Xu, Chen & Feng, Jianwen, 2017. "Exponential synchronization of complex-valued complex networks with time-varying delays and stochastic perturbations via time-delayed impulsive control," Applied Mathematics and Computation, Elsevier, vol. 306(C), pages 22-30.
    3. Zhang, Chunmei & Han, Bang-Sheng, 2020. "Stability analysis of stochastic delayed complex networks with multi-weights based on Razumikhin technique and graph theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    4. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun & Huang, Junjian, 2018. "Synchronization of fractional-order memristor-based complex-valued neural networks with uncertain parameters and time delays," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 105-123.
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    Cited by:

    1. Liu, Zhiguang & Zhu, Quanxin, 2023. "Ultimate boundedness of impulsive stochastic delay differential equations with delayed impulses," Statistics & Probability Letters, Elsevier, vol. 199(C).
    2. Peng, Cheng & Liu, Xiaoqi & Kang, Rui & Wang, Sihan & Gao, Shang, 2023. "Stochastic input-to-state stability for stochastic complex dynamical control networks with impulsive perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Fan, Hongguang & Shi, Kaibo & Zhao, Yi, 2022. "Global μ-synchronization for nonlinear complex networks with unbounded multiple time delays and uncertainties via impulsive control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    4. Miaadi, Foued & Li, Xiaodi, 2021. "Impulsive effect on fixed-time control for distributed delay uncertain static neural networks with leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Yong Tang & Lang Zhou & Jiahui Tang & Yue Rao & Hongguang Fan & Jihong Zhu, 2023. "Hybrid Impulsive Pinning Control for Mean Square Synchronization of Uncertain Multi-Link Complex Networks with Stochastic Characteristics and Hybrid Delays," Mathematics, MDPI, vol. 11(7), pages 1-18, April.

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