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Exponential synchronization of stochastic fuzzy cellular neural networks with time delay in the leakage term and reaction-diffusion. (English) Zbl 1239.93110
Summary: Separate studies have been published on the stability of fuzzy cellular neural networks with time delay in the leakage term and synchronization issue of coupled chaotic neural networks with stochastic perturbation and reaction-diffusion effects. However, no studies that integrate the two fields are existing. Motivated by the achievements from both fields, this paper considers the exponential synchronization problem of coupled chaotic fuzzy cellular neural networks with stochastic noise perturbation, time delay in the leakage term and reaction-diffusion effects using linear feedback control. The Lyapunov stability theory combining with stochastic analysis approaches are employed to derive sufficient criteria ensuring the coupled chaotic fuzzy neural networks to be exponentially synchronized. This paper also presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the proposed scheme.
MSC:
93E03General theory of stochastic systems
93C42Fuzzy control systems
93C73Perturbations in control systems
60H10Stochastic ordinary differential equations
References:
[1]Balasubramaniam P, Kalpana M, Rakkiyappan R. Existence and global asymptotic stability of fuzzy cellular neural networks with time delay in the leakage term and unbounded distributed delays. Circuits Syst Signal Process; in press, doi:10.1007/s00034-011-9288-7.
[2]Balasubramaniam, P.; Vembarasan, V.; Rakkiyappan, R.: Leakage delays in T – S fuzzy cellular neural networks, Neural process lett 33, 111-136 (2011)
[3]Blythe, S.; Mao, X.; Liao, X.: Stability of stochastic delay neural networks, J franklin inst 338, 481-495 (2001) · Zbl 0991.93120 · doi:10.1016/S0016-0032(01)00016-3
[4]Bowong, S.: Stability analysis for the synchronization of chaotic systems with different order: application to secure communications, Phys lett A 326, 102-113 (2004) · Zbl 1161.94389 · doi:10.1016/j.physleta.2004.04.004
[5]Carroll, T. L.; Pecora, L. M.: Synchronization chaotic circuits, IEEE trans circ syst 38, 453-456 (1991)
[6]Chua, L. O.; Yang, L.: Cellular neural networks: theory, IEEE trans circ syst 35, 1257-1272 (1988) · Zbl 0663.94022 · doi:10.1109/31.7600
[7]Chua, L. O.; Yang, L.: Cellular neural networks: applications, IEEE trans circ syst 35, 1273-1290 (1988)
[8]Ding, W.: Synchronization of delayed fuzzy cellular neural networks with impulsive effects, Commun nonlinear sci numer simul 14, 3945-3952 (2009) · Zbl 1221.34194 · doi:10.1016/j.cnsns.2009.02.013
[9]Ding, W.; Han, M.: Synchronization of delayed fuzzy cellular neural networks based on adaptive control, Phys lett A 372, 4674-4681 (2008) · Zbl 1221.94094 · doi:10.1016/j.physleta.2008.04.053
[10]Feki, M.: An adaptive chaos synchronization scheme applied to secure communications, Chaos solitons fractals 18, 141-148 (2003) · Zbl 1048.93508 · doi:10.1016/S0960-0779(02)00585-4
[11]Gopalsamy, K.: Leakage delays in BAM, J math anal appl 325, 1117-1132 (2007) · Zbl 1116.34058 · doi:10.1016/j.jmaa.2006.02.039
[12]Li, C.; Liao, X.; Wong, K.: Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication, Physica D 194, 187-202 (2004) · Zbl 1059.93118 · doi:10.1016/j.physd.2004.02.005
[13]Li, X.; Cao, J.: Delay-dependent stability of neural networks of neutral type with time delay in the leakage term, Nonlinearity 23, 1709-1726 (2010) · Zbl 1196.82102 · doi:10.1088/0951-7715/23/7/010
[14]Li, X.; Rakkiyappan, R.; Balasubramaniam, P.: 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)
[15]Liu, Y.; Tang, W.: Exponential stability of fuzzy cellular neural networks with constant and time-varying delays, Phys lett A 323, 224-233 (2004) · Zbl 1118.81400 · doi:10.1016/j.physleta.2004.01.064
[16]Liu, Z.; Zhang, H.; Wang, Z.: Novel stability criterions of a new fuzzy cellular neural networks with time-varying delays, Neurocomputing 72, 1056-1064 (2009)
[17]Lu, J.: Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions, Chaos solitons fractals 35, 116-125 (2008) · Zbl 1134.35066 · doi:10.1016/j.chaos.2007.05.002
[18]Moskalenko, O. I.; Koronovskii, A. A.; Hramov, A. E.: Generalized synchronization of chaos for secure communication: remarkable stability to noise, Phys lett A 374, 2925-2931 (2010)
[19]Park, J. H.: Robust stability of bidirectional associative memory neural networks with time delays, Phys lett A 349, 494-499 (2006)
[20]Park, J. H.: Further note on global exponential stability of uncertain cellular neural networks with variable delays, Appl math comput 188, 850-854 (2007) · Zbl 1126.34376 · doi:10.1016/j.amc.2006.10.036
[21]Park, J. H.; Kwon, O. M.: Synchronization of neural networks of neutral type with stochastic perturbation, Modern phys lett B 23, 1743-1751 (2009) · Zbl 1167.82358 · doi:10.1142/S0217984909019909
[22]Pecora, L. M.; Carroll, T. L.: Synchronization in chaotic systems, Phys rev lett 64, 821-824 (1990)
[23]Peng, S.: Global attractive periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms, Nonlinear anal RWA 11, 2141-2151 (2010)
[24]Sundar, S.; Minai, A. A.: Synchronization of randomly multiplexed chaotic systems with application to communication, Phys rev lett 85, 5456-5459 (2000)
[25]Ali, M. Syed; Balasubramaniam, P.: Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple discrete and distributed time-varying delays, Commun nonlinear sci numer simul 16, 2907-2916 (2011) · Zbl 1221.34189 · doi:10.1016/j.cnsns.2010.10.011
[26]Tang, Y.; Fang, J.: Robust synchronization in an array of fuzzy delayed cellular neural networks with stochastically hybrid coupling, Neurocomputing 72, 3253-3262 (2009)
[27]Tang, Y.; Fang, J.; Xia, M.; Gu, X.: Synchronization of Takagi – sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays, Appl math modell 34, 843-855 (2010) · Zbl 1185.93145 · doi:10.1016/j.apm.2009.07.015
[28]Wang, J.; Lu, J.: Global exponential stability of fuzzy cellular neural networks with delays and reaction – diffusion terms, Chaos solitons fractals 38, 878-885 (2008) · Zbl 1146.35315 · doi:10.1016/j.chaos.2007.01.032
[29]Wang, L.; Ding, W.: Synchronization for delayed non-autonomous reaction – diffusion fuzzy cellular neural networks, Commun nonlinear sci numer simul 17, 170-182 (2012)
[30]Wang, L.; Ding, W.; Chen, D.: Synchronization schemes of a class of fuzzy cellular neural networks based on adaptive control, Phys lett A 374, 1440-1449 (2010)
[31]Xia, Y.; Yang, Z.; Han, M.: Synchronization schemes for coupled identical Yang – Yang type fuzzy cellular neural networks, Commun nonlinear sci numer simul 14, 3645-3659 (2009) · Zbl 1221.37227 · doi:10.1016/j.cnsns.2009.01.028
[32]Xia, Y.; Yang, Z.; Han, M.: Lag synchronization of unknown chaotic delayed Yang – Yang-type fuzzy neural networks with noise perturbation based on adaptive control and parameter identification, IEEE trans neural networks 20, 1165-1180 (2009)
[33]Yang, T.; Yang, L.: The global stability of fuzzy neural network, IEEE trans circ syst 43, 880-883 (1996)
[34]Yang T, Yang L, Wu C, Chua LO. Fuzzy cellular neural networks: theory. In: Proceedings of IEEE international workshop on cellular neural networks and applications; 1996. p. 181 – 186.
[35]Yang T, Yang L, Wu C, Chua LO. Fuzzy cellular neural networks: applications. In: Proceedings of IEEE international workshop on cellular neural networks and applications; 1996. p. 225 – 230.
[36]Yu, F.; Jiang, H.: Global exponential synchronization of fuzzy cellular neural networks with delays and reaction – diffusion terms, Neurocomputing 74, 509-515 (2011)
[37]Yuan, K.; Cao, J.; Deng, J.: Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays, Neurocomputing 69, 1619-1627 (2006)
[38]Zhang, Q.; Xiang, R.: Global asymptotic stability of fuzzy cellular neural networks with time-varying delays, Phys lett A 372, 3971-3977 (2008) · Zbl 1220.34098 · doi:10.1016/j.physleta.2008.01.063