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New synchronization criteria for an array of neural networks with hybrid coupling and time-varying delays. (English) Zbl 1482.34178

Summary: This paper is concerned with the global exponential synchronization for an array of hybrid coupled neural networks with time-varying leakage delay, discrete and distributed delays. Applying a novel Lyapunov functional and the property of outer coupling matrices of the neural networks, sufficient conditions are obtained for the global exponential synchronization of the system. The derived synchronization criteria are closely related with the time-varying delays and the coupling structure of the networks. The maximal allowable upper bounds of the time-varying delays can be obtained guaranteeing the global synchronization for the neural networks. The method we adopt in this paper is different from the commonly used linear matrix inequality (LMI) technique, and our synchronization conditions are new, which are easy to check in comparison with the previously reported LMI-based ones. Some examples are given to show the effectiveness of the obtained theoretical results.

MSC:

34K24 Synchronization of functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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[1] P. Balasubramaniam, M. Kalpana, R. Rakkiyappan, Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays, Math. Comput. Modelling, 53:839-853, 2011. · Zbl 1217.34116
[2] P. Balasubramaniam, V. Vembarasan, Asymptotic stability of BAM neural networks of neutraltype with impulsive effects and time delay in the leakage term, Int. J. Comput. Math., 88:3271- 3291, 2011. · Zbl 1247.34122
[3] P. Balasubramaniam, V. Vembarasan, Synchronization of recurrent neural networks with mixed time-delays via output coupling with delayed feedback, Nonlinear Dyn., 70:677-691, 2012. · Zbl 1267.93138
[4] P. Balasubramaniam, V. Vembarasan, R. Rakkiyappan, Leakage delays in T-S fuzzy cellular neural networks, Neural Process. Lett., 33:111-136, 2011.
[5] P. Balasubramaniam, V. Vembarasan, R. Rakkiyappan, Global robust asymptotic stability analysis of uncertain switched Hopfield neural networks with time delay in the leakage term, Neural Comput. Appl., 21:1593-1616, 2012.
[6] A. Barabási, R. Albert, Emergence of scaling in random networks, Science, 286:509-512, 1999. Nonlinear Anal. Model. Control, 21(1):57-76 74Y. Du, R. Xu · Zbl 1226.05223
[7] J. Cao, A. Alofi, A. Al-Mazrooei, A. Elaiw, Synchronization of switched interval networks and applications to chaotic neural networks, Abstr. Appl. Anal., 2013, Article ID 940573, 11 pp., 2013. · Zbl 1421.93067
[8] J. Cao, G. Chen, P. Li, Global synchronization in an array of delayed neural networks with hybrid coupling, IEEE Trans. Syst. Man Cybern., 38:488-498, 2008.
[9] J. Cao, L. Li, Cluster synchronization in an array of hybrid coupled neural networks with delay, Neural Netw., 22:335-342, 2009. · Zbl 1338.93284
[10] J. Cao, Y. Wan, Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays, Neural Netw., 53:165-172, 2014. · Zbl 1322.93087
[11] J. Cao, Z. Wang, Y. Sun, Synchronization in an array of linearly stochastically coupled networks with time delays, Physica A, 385:718-728, 2007.
[12] Y. Du, R. Xu, Robust synchronization of an array of neural networks with hybrid coupling and mixed time delays, ISA Trans., 53(4):1015-1023, 2014.
[13] Q. Gan, Exponential synchronization of stochastic neural networks with leakage delay and reaction-diffusion terms via periodically intermittent control, Chaos, 22, 013124, 2012. · Zbl 1331.92015
[14] Q. Gan, Y. Liang, Synchronization of chaotic neural networks with time delay in the leakage term and parametric uncertainties based on sampled-data control, J. Franklin Inst., 349:1955- 1971, 2012. · Zbl 1300.93113
[15] D. Gong, H. Zhang, Z. Wang, B. Huang, Pinning synchronization for a general complex networks with multiple time-varying coupling delays, Neural Process. Lett., 35:221-231, 2012.
[16] K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic, Dordrecht, 1992. · Zbl 0752.34039
[17] J. Hajnal, Weak ergodicity in non-homogenous Markov chains, Math. Proc. Camb. Philos. Soc., 54:233-246, 1958. · Zbl 0082.34501
[18] Y. Hatano, M. Mesbahi, Agreement over random networks, IEEE Trans. Autom. Control, 50:1867-1872, 2005. · Zbl 1365.94482
[19] N. Li, J. Cao, Periodically intermittent control on robust exponential synchronization for switched interval coupled networks, Neurocomputing, 131:52-58, 2014.
[20] X. Li, X. Fu, R. Rakkiyappan, Delay-dependent stability analysis for a class of dynamical systems with leakage delay and nonlinear perturbations, Appl. Math. Comput., 226:10-19, 2014. · Zbl 1354.34127
[21] X. Li, R. Rakkiyappanb, P. Balasubramaniam, Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations, J. Franklin Inst., 348:135-155, 2011. · Zbl 1241.92006
[22] X. Liao, Theory and Application of Stability for Dynamical Systems, National Defence and Industry Press, Beijing, 2000 (in Chinese). · Zbl 0966.34001
[23] B. Liu, T. Chen, Consensus in networks of multiagents with cooperation and competition via stochastically swithching topologies, IEEE Trans. Neural Netw., 19:1967-1973, 2008. http://www.mii.lt/NA New synchronization criteria for an array of neural networks75
[24] B. Liu, W. Lu, T. Chen, Synchronization in complex networks with stochastically swithching coupling structures, IEEE Trans. Autom. Control, 57:754-760, 2012. · Zbl 1369.93033
[25] Y. Liu, Z. Wang, J. Liang, X. Liu, Synchronization of coupled neutral-type neural networks with jumping-mode-dependent discrete and unbounded distributed delays, IEEE Trans. Cybern., 43:102-114, 2013.
[26] J. Lu, J. Kurths, J. Cao, N. Mahdavi, Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy, IEEE Trans. Neural Netw. Learn. Syst., 23:285-292, 2012.
[27] J. Mei, M. Jiang, W. Xu, B. Wang, Finite-time synchronization control of complex dynamical networks with time delay, Commun. Nonlinear Sci. Numer. Simul., 18:2462-2478, 2013. · Zbl 1311.34157
[28] M.J. Park, O.M. Kwon, Ju H. Park, S.M. Lee, E.J. Cha, Synchronization criteria for coupled neural networks with interval time-varying delays and leakage delay, Appl. Math. Comput., 218:6762-6775, 2012. · Zbl 1401.93021
[29] M.J. Park, O.M. Kwon, Ju H. Park, S.M. Lee, E.J. Cha, Synchronization criteria for coupled stochastic neural networks with time-varying delays and leakage delay, J. Franklin Inst., 349:1699-1720, 2012. · Zbl 1254.93012
[30] M.J. Park, O.M. Kwon, Ju H. Park, S.M. Lee, E.J. Cha, On synchronization criterion for coupled discrete-time neural networks with interval time-varying delays, Neurocomputing, 99:188-196, 2013. · Zbl 1274.93251
[31] Q. Song, Synchronization analysis in an array of asymmetric neural networks with time-varying delays and nonlinear coupling, Appl. Math. Comput., 216:1605-1613, 2010. · Zbl 1194.34145
[32] Y. Sun, W. Li, J. Ruan, Generalized outer synchronization between complex dynamical networks with time delay and noise perturbation, Commun. Nonlinear Sci. Numer. Simul., 18:989-998, 2013. · Zbl 1260.93004
[33] Y. Tang, W.K. Wong, Distributed synchronization of coupled neural networks via randomly occurring control, IEEE Trans. Neural Netw. Learn. Syst., 24:435-447, 2013.
[34] V. Vembarasan, P. Balasubramaniam, Chaotic synchronization of Rikitake system based on T-S fuzzy control techniques, Nonlinear Dyn., 74:31-44, 2013. · Zbl 1281.34097
[35] Z. Wang, T. Li, H. Zhang, Fault tolerant synchronization for a class of complex interconnected neural networks with delay, Int. J. Adapt. Control Signal Process., 28(10):859-881, 2014. · Zbl 1337.93030
[36] H. Wang, Q. Song, Synchronization for an array of coupled stochastic discrete-time neural networks with mixed delays, Neurocomputing, 74:1572-1584, 2011.
[37] K. Wang, Z. Teng, H. Jiang, Adaptive synchronization in an array of linearly coupled neural networks with reaction-diffusion terms and time delays, Commun. Nonlinear Sci. Numer. Simul., 17:3866-3875, 2012. · Zbl 1253.92004
[38] S. Wang, H. Yao, M. Sun, Cluster synchronization of time-varying delays coupled complex networks with nonidentical dynamical nodes, J. Appl. Math., 2012, Article ID 958405, 12 pp., 2012. · Zbl 1244.93114
[39] G. Wang, Q. Yin, Y. Shen, Exponential synchronization of coupled fuzzy neural networks with disturbances and mixed time-delays, Neurocomputing, 106:77-85, 2013. Nonlinear Anal. Model. Control, 21(1):57-76 76Y. Du, R. Xu
[40] Z. Wang, H. Zhang, Synchronization stability in complex interconnected neural networks with nonsymmetric coupling, Neurocomputing, 108:84-92, 2013.
[41] Z. Wang, H. Zhang, B. Jiang, LMI-based approach for global asymptotic stability analysis of recurrent neural networks with various delays and structures, IEEE Trans. Neural Netw., 22:1032-1045, 2011.
[42] J. Wang, H. Zhang, Z. Wang, B. Wan, Local exponential synchronization in complex dynamical networks with time-varying delay and hybrid coupling, Appl. Math. Comput., 225:16-32, 2013. · Zbl 1336.93024
[43] D. Watts, S. Strogatz, Collective dynamics of ‘small-world’ networks, Nature, 393:440-442, 1998. · Zbl 1368.05139
[44] C. Wu, Synchronization and convergence of linear dynamics in random directed networks, IEEE Trans. Autom. Control, 51:1207-1210, 2006. · Zbl 1366.93537
[45] Z. Wu, P. Shi, H. Su, J. Chu, Sampled-data exponential synchronization of complex dynamical networks with time-varying coupling delay, IEEE Trans. Neural Netw. Learn. Syst., 24:1177- 1187, 2013.
[46] X. Yang, J. Cao, J. Lu, Synchronization of markovian coupled neural networks with nonidentical node-delays and random coupling strengths, IEEE Trans. Neural Netw. Learn. Syst., 23:60-71, 2012.
[47] X. Yang, J. Cao, J. Lu, Synchronization of randomly coupled neural networks with Markovian jumping and time-delay, IEEE Trans. Circuits Syst., I, Fundam. Theory Appl., 60:363-376, 2013. · Zbl 1468.93189
[48] X. Yang, J. Cao, Z. Yang, Synchronization of coupled reaction-diffusion neural networks with time-varying delays via pinning-impulsive controller, SIAM J. Control Optim., 51:3486-3510, 2013. · Zbl 1281.93052
[49] J. Yi, Y. Wang, J. Xiao, Y. Huang, Exponential synchronization of complex dynamical networks with markovian jump parameters and stochastic delays and its application to multi-agent systems, Commun. Nonlinear Sci. Numer. Simul., 18:1175-1192, 2013. · Zbl 1269.34058
[50] H. Zhang, D. Gong, B. Chen, Z. Liu, Synchronization for coupled neural networks with interval delay: a novel augmented Lyapunov-Krasovskii functional method, IEEE Trans. Neural Netw. Learn. Syst., 24:58-70, 2013.
[51] Y. Zhang, A. Gu, S. Xu, Global exponential adaptive synchronization of complex dynamical networks with neutral-type neural network nodes and stochastic disturbances, IEEE Trans. Circuits Syst., I, Fundam. Theory Appl., 99:1-10, 2013.
[52] W. Zhang, Y. Tang, Q. Miao, W. Du, Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects, IEEE Trans. Neural Netw. Learn. Syst., 24:1316-1326, 2013.
[53] H. Zhang, M. Zhao, Z. Wang, Z. Wu, Adaptive synchronization of an uncertain coupling complex network with time-delay, Nonlinear Dyn., 77(3):643-653, 2014. · Zbl 1314.93047
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