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Synchronization of delayed neural networks with hybrid coupling via partial mixed pinning impulsive control

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  • Yi, Chengbo
  • Feng, Jianwen
  • Wang, Jingyi
  • Xu, Chen
  • Zhao, Yi

Abstract

This paper investigates the synchronization problem of a class of general hybrid coupling delayed neural networks with internal delay as well as coupling delay. A general hybrid coupling term involving current-state coupling, discrete-delay coupling and distributed-delay coupling is considered. The partial mixed pinning impulsive control is proposed for achieving synchronization, which is combined with the advantage of pinning impulsive control and two impulsive effects simultaneously (i.e. synchronization and desynchronization). In order to handle the difficulties of multi-time delays, some generalized differential inequalities about time-varying delays are established. By using Lyapunov functional method and applying a mixed pinning impulsive control scheme, some sufficient conditions are derived to guarantee global synchronization of the neural networks. Moreover, our results can cover and extend the previous related works. Finally, numerical examples are also given to illustrate the efficiency of our methods and the theoretical results.

Suggested Citation

  • Yi, Chengbo & Feng, Jianwen & Wang, Jingyi & Xu, Chen & Zhao, Yi, 2017. "Synchronization of delayed neural networks with hybrid coupling via partial mixed pinning impulsive control," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 78-90.
    • Handle: RePEc:eee:apmaco:v:312:y:2017:i:c:p:78-90
    DOI: 10.1016/j.amc.2017.04.030
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    References listed on IDEAS

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    1. Wang, Xiao Fan & Chen, Guanrong, 2002. "Pinning control of scale-free dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 521-531.
    2. Feng, Jianwen & Yang, Pan & Zhao, Yi, 2016. "Cluster synchronization for nonlinearly time-varying delayed coupling complex networks with stochastic perturbation via periodically intermittent pinning control," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 52-68.
    3. Shen, Mouquan & Yan, Shen & Zhang, Guangming & Park, Ju H., 2016. "Finite-time H∞ static output control of Markov jump systems with an auxiliary approach," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 553-561.
    4. Li, Ping & Cao, Jinde & Wang, Zidong, 2007. "Robust impulsive synchronization of coupled delayed neural networks with uncertainties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 261-272.
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    Cited by:

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    2. Guo, Beibei & Wu, Yinhu & Xiao, Yu & Zhang, Chiping, 2018. "Graph-theoretic approach to synchronizing stochastic coupled systems with time-varying delays on networks via periodically intermittent control," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 341-357.
    3. 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.
    4. Xia, Xue & Bai, Jing & Li, Xiaohe & Wen, Guoguang, 2023. "Containment control for fractional order MASs with nonlinearity and time delay via pull-based event-triggered mechanism," Applied Mathematics and Computation, Elsevier, vol. 454(C).
    5. Dong, Shiyu & Shi, Kaibo & Wen, Shiping & Shen, Yuan & Zhong, Shouming, 2023. "Almost surely synchronization of directed coupled neural networks via stochastic distributed delayed impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Fu, Qianhua & Zhong, Shouming & Shi, Kaibo, 2021. "Exponential synchronization of memristive neural networks with inertial and nonlinear coupling terms: Pinning impulsive control approaches," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    7. Wei, Tengda & Lin, Ping & Zhu, Quanxin & Yao, Qi, 2021. "Instability of impulsive stochastic systems with application to image encryption," Applied Mathematics and Computation, Elsevier, vol. 402(C).

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