Abstract
In this paper, we mainly investigate synchronization of complex-valued neural networks (CVNNs) with time delays and impulsive effects. By using Lyapunov method and some inequality techniques, some sufficient conditions for the synchronization of CVNNs with time delays and impulsive effects are proposed. Finally, a numerical example based on small-world networks is presented to demonstrate correctness of the theoretical results.





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Cao JD, Wan Y (2014) Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays. Neural Netw 53:165–172
Li LL, Cao JD (2011) Cluster synchronization in an array of coupled stochastic delayed neural networks via pinning control. Neurocomputing 74:846–856
Yuan DM, Ho DWC, Hong YG (2016) On convergence rate of distributed stochastic gradient algorithm for convex optimization with inequality constraints. SIAM J Control Optim 54(5):2872–2892
Lu JQ, Ding CD, Lou JG, Cao JD (2015) Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers. J Frankl Inst 352:5014–5041
Liu XY, Cao JD, Yu WW, Song Q (2016) Nonsmooth finite-time synchronization of switched coupled neural networks. IEEE Trans Cybern 46(10):2360–2371
Yuan DM, Hong YG, Ho DWC, Jiang GP (2018) Optimal distributed stochastic mirror descent for strongly convex optimization. Automatica 90:196–203
Wu W, Chen TP (2009) Partial synchronization in linearly and symmetrically coupled ordinary differential systems. Phys D 238:355–364
Li LL, Ho DWC, Cao JD, Lu JQ (2016) Pinning cluster synchronization of an array of coupled neural networks under event-triggered mechanism. Neural Netw 76:1–12
Huang C, Ho DWC, Lu JQ (2015) Partial-information-based synchronization analysis for complex dynamical networks. J Frankl Inst 352:3458–3475
Lu JQ, Ho DWC, Cao JD, Kurths J (2013) Single impulsive controller for globally exponential synchronization of dynamical networks. Nonlinear Anal: Real World Appl 14:581–593
Lu WL, Chen TP (2011) Synchronization of coupled connected neural networks with delays. IEEE Trans Circuits Syst I 51(12):2491–2503
Huang C, Ho DWC, Lu JQ, Kurths J (2015) Pinning synchronization in T-S fuzzy complex networks with partial and discrete-time couplings. IEEE Trans Fuzzy Syst 23(4):1274–1285
Chen TP, Liu XW, Lu WL (2007) Pinning complex networks by a single controller. IEEE Trans Circuits Syst I 54(6):1317–1326
Huang C, Wang W, Cao JD, Lu JQ (2018) Synchronization-based passivity of partially coupled neural networks with event-triggered communication. Neurocomputing 319:134–143
Lu JQ, Ho DWC, Cao JD, Kurths J (2011) Exponential synchronization of linearly coupled neural networks with impulsive disturbances. IEEE Trans Neural Netw 22(2):329–335
Wang YQ, Lu JQ, Liang JL, Cao JD, Perc M (2019) Pinning synchronization of nonlinear coupled Lur’e networks under hybrid impulses. IEEE Trans Circuits Syst II: Express Briefs 66(3):432–436
Yang JJ, Lu JJ, Li LL, Liu Y, Wang Z, Alsaadi FE (2019) Event-triggered control for the synchronization of Boolean control networks. Nonlinear Dyn. https://doi.org/10.1007/s11071-019-04857-2
Rakkiyappan R, Velmurugan G, Li XD (2015) Complete stability analysis of complex-valued neural networks with time delays and impulses. Neural Process Lett 41:435–468
Hu J, Wang J (2012) Global stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 23(6):853–865
Fang T, Sun JT (2007) Further investigate the stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Autom Control 52(9):1680–1685
Bohner M, Rao VSH, Sanyal S (2011) Global stability of complex-valued neural networks on time scales. Differ Equ Dyn Syst 19(1, 2):3–11
Song QK, Yan H, Zhao ZJ, Liu YR (2016) Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. Neural Netw 81:1–10
Gong WQ, Liang JL, Zhang CJ, Cao JD (2016) Nonlinear measure approach for the stability analysis of complex-valued neural networks. Neural Process Lett 44(2):539–554
Yan MM, Qiu JL, Chen XY, Chen X, Yang CD, Zhang AC, Alsaadi F (2018) The global exponential stability of the delayed complex-valued neural networks with almost periodic coefficients and discontinuous activations. Neural Process Lett 48(1):577–601
Yang XS, Cao JD, Qiu JL (2015) \(P\)th moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control. Neural Netw 65:80–91
Li YY (2017) Impulsive synchronization of stochastic neural networks via controlling partial states. Neural Process Lett 46:59–69
Lu JQ, Ho DWC, Cao JD (2010) A unified synchronization criterion for impulsive dynamical networks. Automatica 46:1215–1221
Lu JQ, Wang ZD, Cao JD, Ho DWC, Kurths J (2012) Pinning impulsive stabilization of nonlinearly dynamical networks with time-varying delay. Int J Bifurc Chaos 22(7):1250176
Li YY, Lou J, Wang Z, Alsaadi FE (2018) Synchronization of nonlinearly coupled dynamical networks under hybrid pinning impulsive controllers. J Frankl Inst 355(14):6520–6530
Horn R, Johnson C (1990) Matrix analysis. Cambridge University Press, Cambridge
Acknowledgements
The work was jointly supported by the National Natural Science Foundation of China under Grants 61503115 and the Fundamental Research Funds for the Central Universities under Grants JZ2017HGTB0188.
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Li, L., Mu, G. Synchronization of Coupled Complex-Valued Impulsive Neural Networks with Time Delays. Neural Process Lett 50, 2515–2527 (2019). https://doi.org/10.1007/s11063-019-10028-6
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DOI: https://doi.org/10.1007/s11063-019-10028-6