Abstract
The problem of exponential module-phase synchronization of complex-valued neural networks (CVNNs) with time-varying delay and stochastic perturbations was investigated. The model of CVNNs with time-varying delay and stochastic perturbations was considered. The error system was deduced and the module-phase synchronization was defined. Based on the principle of Lyapunov stability theory, the appropriate controller was designed to control the CVNNs. Finally, the effectiveness and reliability of the method were verified by the numerical simulations.
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Du Y, Liu J, and Fu S, Information transmitting and cognition with a spiking neural network model, Chinese Phys. Lett., 2018, 35(9): 090502.
Ruan X, Wu H, Li N, et al., Convergence analysis in sense of Lebesgue-pnorm of decentralized non-repetitive iterative learning control for linear large-scale systems, Journal of Systems Science and Complexity, 2009, 22(3): 422–434.
Qiao C, Liang D, and Sun K, Dynamics analysis for generic projection continuous-time RNNs with bounded matrices, Journal of Systems Science and Complexity, 2015, 28(4): 799–812.
Geidarov P S, Neural networks with image recognition by pairs, Optical Memory and Neural Networks, 2018, 27(2): 113–119.
Roli A, Villani M, Filisetti A, et al., Dynamical criticality: Overview and open questions, Journal of Systems Science and Complexity, 2018, 31(3): 647–663.
Xu G, Xu J, Xiu C, et al., Secure communication based on the synchronous control of hysteretic chaotic neuron, Neurocomputing, 2017, 227: 108–112.
Elkatatny S, Tariq Z, Mahmoud M, et al., Development of new mathematical model for compressional and shear sonic times from wireline log data using artificial intelligence neural networks (white box), Arab. J. Sci. Eng., 43 (11): 6375–6389.
Zhao Y, Lu Q, and Feng Z, Stability for the mix-delayed Cohen-Grossberg neural networks with nonlinear impulse, Journal of Systems Science and Complexity, 2010, 23(3): 665–680.
Luo S, Li S, and Tajaddodianfar F, Chaos and nonlinear feedback control of the arch microelectromechanical system, Journal of Systems Science and Complexity, 2018, 31(6): 1510–1524.
Ahmed H, Ushirobira R, and Efimov D, Experimental study of the robust global synchronization of Brockett oscillators, Eur. Phys. J-Spec. Top., 2017, 226(15): 3199–3210.
Zhang Z and Ren L, New sufficient conditions on global asymptotic synchronization of inertial delayed neural networks by using integrating inequality techniques, Nonlinear Dynam., 2019, 40(2): 905–917.
Moreira C A and Aguiar M A M D, Global synchronization of partially forced Kuramoto oscillators on Networks, Physica A, 2019, 514: 487–496.
Sedov A S, Medvednik R S, and Raeva S N, Significance of local synchronization and oscillatory processes of thalamic neurons in goal-directed human behavior, Fiziologiia Cheloveka, 2014, 40(1): 1–7.
Zhou W, Gao Y, Tong D, et al., Adaptive exponential synchronization in pth moment of neutral-type neural networks with time delays and Markovian switching, Int. J. Control Autom., 2013, 11(4): 845–851.
Xu Y, Yang H, Tong D, et al., Adaptive exponential synchronization in p th moment for stochastic time varying multi-delayed complex networks, Nonlinear Dynam., 2013, 73(3): 1–15.
Xie D and Jiang Y, Global exponential synchronization of complex-valued neural networks with time delays via matrix measure method, Neural Process Lett., 2018, 49(1): 187–201.
Zhang C, Wang X, Luo C, et al, Robust outer synchronization between two nonlinear complex networks with parametric disturbances and mixed time-varying delays, Physica A, 2018, 494: 251–264.
Nian F, Wang X, Niu Y, et al., Module-phase synchronization in complex dynamic system, Appl. Math. Comput., 2010, 217(6): 2481–2489.
Zhang H, Wang X Y, and Li X H, Synchronization of complex-valued neural network with sliding mode control, J. Franklin I., 2016, 353(2): 345–358.
Zhou C, Zhang W, Yang X, et al., Finite-time synchronization of complex-valued neural networks with mixed delays and uncertain perturbations, Neural Process Lett., 2017, 46(1): 1–21.
Zhou J, Lu J, and Lu J, Adaptive synchronization of an uncertain complex dynamical network, IEEE T. Automat. Contr., 2005, 51(4): 652–656.
Liu D, Zhu S, and Ye E, Synchronization stability of memristor-based complex-valued neural networks with time delays, Neural Networks, 2017, 96(4): 115–127.
Liu B, Hill D J, Zhang C, et al., Stabilization of discrete-time dynamical systems under event-triggered impulsive control with and without time-delays, Journal of Systems Science and Complexity, 2018, 31(1): 130–146.
Zhang L, Yang X, Xu C, et al., Exponential synchronization of complex-valued complex networks with time-varying delays and stochastic perturbations via time-delayed impulsive control, Appl. Math. Comput., 2017, 306: 22–30.
Nian F and Zhao Q, Pinning synchronization with low energy cost, Commun. Nonlinear Sci., 2014, 9(4): 930–940.
Liang Y and Wang X, Synchronizability on complex networks via pinning control, Pramana, 2013, 80(4): 593–606.
Nian F, Liu X, and Zhang Y, Sliding mode synchronization of fractional-order complex chaotic system with parametric and external disturbances, Chaos Soliton Fract., 2018, 116: 22–28.
Khan A, Combination synchronization of Genesio time delay chaotic system via robust adaptive sliding mode control, Int. J. Control, 2018, 6(2): 758–767.
Zhou C, Zhang W, Yang X, et al., Finite-time synchronization of complex-valued neural networks with mixed delays and uncertain perturbations, Neural Process Lett., 2017, 46(1): 271–291.
Zhang Z, Li A, and Yu S, Finite-time synchronization for delayed complex-valued neural networks via integrating inequality method, Neurocomputing, 2018, 318: 248–260.
Li X, Fang J A, and Li H, Exponential adaptive synchronization of stochastic memristive chaotic recurrent neural networks with time-varying delays, Neurocomputing, 2017, 267: 396–405.
Bao H, Park J H, and Cao J, Synchronization of fractional-order complex-valued neural networks with time delay, Neural Networks, 2016, 81: 16–28.
Liu D, Zhu S, and Ye E, Synchronization stability of memristor-based complex-valued neural networks with time delays, Neural Netw., 2017, 96: 115–127.
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This research is supported by the National Natural Science Foundation of China under Grant No. 61863025, International S & T Cooperation Projects of Gansu province under Grant No. 144WCGA166, and Longyuan Young Innovation Talents and the Doctoral Foundation of LUT.
This paper was recommended for publication by Editor SUN Jian.
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Nian, F., Li, J. The Module-Phase Synchronization of Complex-Valued Neural Networks with Time-Varying Delay and Stochastic Perturbations. J Syst Sci Complex 34, 2139–2154 (2021). https://doi.org/10.1007/s11424-021-9024-8
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DOI: https://doi.org/10.1007/s11424-021-9024-8