ZHANG Zhishu, GAO Yan. Adaptive Synchronization of Neutral-Type Coupled Neural Networks With Stochastic Perturbations and Markovian Jumpings[J]. Applied Mathematics and Mechanics, 2020, 41(12): 1381-1391. doi: 10.21656/1000-0887.410079
Citation: ZHANG Zhishu, GAO Yan. Adaptive Synchronization of Neutral-Type Coupled Neural Networks With Stochastic Perturbations and Markovian Jumpings[J]. Applied Mathematics and Mechanics, 2020, 41(12): 1381-1391. doi: 10.21656/1000-0887.410079

Adaptive Synchronization of Neutral-Type Coupled Neural Networks With Stochastic Perturbations and Markovian Jumpings

doi: 10.21656/1000-0887.410079
  • Received Date: 2020-03-16
  • Rev Recd Date: 2020-04-27
  • Publish Date: 2020-12-01
  • The adaptive synchronization problem of neutral-type neural networks with time-varying delays and stochastic perturbations was discussed. Stochastic perturbations were described as the Brownian motion. Through the Lyapunov stability theory, the LMI analysis techniques and the matrix theory were used to study the adaptive synchronization of neutral-type neural networks with stochastic perturbations and Markovian jumpings. The sufficient conditions for the system synchronization were given and proved. The criterion for adaptive synchronization of neutral-type neural networks with time-varying delays and stochastic perturbations was obtained. Finally, numerical examples show the effectiveness and applicability of the proposed approach.
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  • [1]
    ZUO Z Q, YANG C L, WANG Y J. A new method for stability analysis of recurrent neural networks with interval time-varying delay[J]. IEEE Transactions on Neural Networks,2010,21(2): 339-344.
    [2]
    BAI Y Q, CHEN J. New stability criteria for recurrent neural networks with interval time-varying delay[J]. Neurocomputing,2013,121(9): 179-184.
    [3]
    HE Y, LIU G, REES D. New delay-dependent stability criteria for neural networks with time-varying delay[J]. IEEE Transactions on Neural Networks,2007,18(1): 31-314.
    [4]
    ZHOU W, ZHU Q, SHI P, et al. Adaptive synchronization for neutral-type neural networks with stochastic perturbation and Markovian switching parameters[J]. IEEE Transactions on Cybernetics,2014,44(12): 2848-2860.
    [5]
    WANG J L, WU H N, GUO L. Novel adaptive strategies for synchronization of linearly coupled neural networks with reaction-diffusion terms[J]. IEEE Transactions on Neural Networks and Learning Systems,2014,25(2): 429-440.
    [6]
    周军, 童东兵, 陈巧玉. 基于事件触发控制带有多时变时滞的主从系统同步[J]. 应用数学和力学, 2019,40(12): 1389-1398. (ZHOU Jun, TONG Dongbing, CHEN Qiaoyu. Synchronization of master-slave systems with multiple time-varying delays based on the event-trigger[J]. Applied Mathematics and Mechanics,2019,40(12): 1389-1398. (in Chinese))
    [7]
    SAMIDURAI R, RAJAVEL S, SRIRAMAN R, et al. Novel results on stability analysis of neutral-type neural networks with additive time-varying delay components and leakage delay[J]. International Journal of Control, Automation and Systems,2017,15(4): 1888-1900.
    [8]
    BALASUBRAMANIAM P, VEMBARASAN V. Asymptotic stability of BAM neural networks of neutral-type with impulsive effects and time delay in the leakage term[J]. International Journal of Computer Mathematics,2011,88(15): 3271-3291.
    [9]
    WANG X H, LI S Y, XU D V. Globally exponential stability of periodic solutions for impulsive neutral-type neural networks with delays[J]. Nonlinear Dynamics,2011, 64(1/2): 65-75.
    [10]
    ZHOU W N, GAO Y, TONG D B, et al. Adaptive exponential synchronization in p th moment of neutral-type neural networks with time delays and Markovian switching[J]. International Journal of Control, Automation and Systems,2013,11(4): 845-851.
    [11]
    ZHANG Y, GU D, XU S. Global exponential adaptive synchronization of complex dynamical networks with neutral-type neural network nodes and stochastic disturbances[J]. IEEE Transactions on Circuits and Systems I: Regular Papers,2013, 60(10): 2709-2718.
    [12]
    RAO R F, ZHONG S M, WANG X R. Stochastic stability criteria with LMI conditions for Markovian jumping impulsive BAM neural networks with mode-dependent time-varying delays and nonlinear reaction-diffusion[J]. Communications in Nonlinear Science and Numerical Simulation,2014,19(1): 258-273.
    [13]
    WU T, XIONG L I, CAO JINDE, et al. New stability and stabilization conditions for stochastic neural networks of neutral type with Markovian jumping parameters[J]. Journal of the Franklin Institute,2018,355(17): 8462-8483.
    [14]
    HUANG H Y, DU Q S, KANG X B. Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays[J]. ISA Transaction s, 2013, 52(6): 759-767.
    [15]
    MAHARAJAN C, RAJA R, CAO J D, et al. Global exponential stability of Markovian jumping stochastic impulsive uncertain BAM neural networks with leakage, mixed time delays, and α-inverse H?lder activation functions[J]. Advances in Difference Equations,2018,2018(1): 1-31.
    [16]
    JIANG G, TANG W K, CHEN G. A state-observer-based approach for synchronization in complex dynamical networks[J]. IEEE Transactions on Circuits and Systems I: Regular Papers,2006,53(12): 2739-2745.
    [17]
    阿子阿英, 饶若峰, 赵锋, 等. 具概率延迟反馈金融系统的脉冲控制[J]. 应用数学和力学, 2019, 40(12): 1409-1416. (AZI Aying, RAO Ruofeng, ZHAO Feng, et al. Impulse control of financial systems with probabilistic delay feedback[J]. Applied Mathematics and Mechanics,2019,40(12): 1409-1416. (in Chinese))
    [18]
    YANG X, CAO J, LU J. Stochastic synchronization of complex networks with nonidentical nodes via hybrid adaptive and impulsive control[J]. IEEE Transactions on Circuits and Systems I: Regular Papers,2012,59(2): 371-384.
    [19]
    ZHANG Q, LU J, TSE C K. Adaptive feedback synchronization of a general complex dynamical network with delayed nodes[J]. IEEE Transactions on Circuits and Systems Ⅱ: Express Briefs,2008,55(2): 183-187.
    [20]
    SHI M, LI J M, HE C, et al. Synchronization of complex dynamical networks with nonidentical nodes and derivative coupling via distributed adaptive control[J]. Mathematical Problems in Engineering,2013,2013(10): 172608. DOI: 10.1155/2013/172608.
    [21]
    LEE T H, WU Z G, PARK J H. Synchronization of a complex dynamical network with coupling time-varying delays via sampled-data control[J]. Applied Mathematics and Computation,2012,219(3): 1354-1366.
    [22]
    SUN X J, FENG Z H, LIU X L. Pinning adaptive synchronization of neutral-type coupled neural networks with stochastic perturbation[J]. Advances in Difference Equations,2014,2014(1): 1-13.
    [23]
    PAN L J, CAO J, AI-JUBOORI UI A, et al. Cluster synchronization of stochastic neural networks with delay via pinning impulsive control[J]. Neurocomputing,2019,366(13): 109-117.
    [24]
    WANG Y L, CAO J D, HU J Q. Stochastic synchronization of coupled delayed neural networks with switching topologies via single pinning impulsive control[J]. Neural Computing and Applications,2015,26(7): 1739-1749.
    [25]
    WU X, XU C. Cluster synchronization of nonlinearly coupled neural networks with hybrid time-varying delays and stochastic perturbations via pinning control[J]. Journal of Convergence Information Technology,2012,7(6): 101-111.
    [26]
    ZENG H B, PARK H J, ZHANG C F, et al. Stability and dissipativity analysis of static neural networks with interval time-varying delay[J]. Journal of the Franklin Institute,2015,352(3): 1284-1295.
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