In this paper, the exponential synchronization problem for fuzzy Cohen-Grossberg neural networks with time-varying delays, stochastic noise disturbance, and reaction-diffusion effects are investigated. By introducing a novel Lyapunov-Krasovskii functional with the idea of delay partitioning, a periodically intermittent controller is developed to derive sufficient conditions ensuring the addressed neural networks to be exponentially synchronized in terms of p-norm. The results extend and improve upon earlier work. A numerical example is provided to show the effectiveness of the proposed theories.
References
1.
Cohen
, M.
, and Grossberg
, S.
, 1983
, “Absolute Stability and Global Pattern Formation and Parallel Memory Storage by Competitive Neural Networks
,” IEEE Trans. Syst. Man Cybern.
, 13
(5
), pp. 815
–821
.10.1109/TSMC.1983.63130752.
Arik
, S.
, and Orman
, Z.
, 2005
, “Global Stability Analysis of Cohen-Grossberg Neural Networks With Time Varying Delays
,” Phys. Lett. A
, 341
(5–6
), pp. 410
–421
.10.1016/j.physleta.2005.04.0953.
Balasubramaniam
, P.
, and Syed Ali
, M.
, 2010
, “Robust Exponential Stability of Uncertain Fuzzy Cohen-Grossberg Neural Networks With Time-Varying Delays
,” Fuzzy Sets Syst.
, 161
(4
), pp. 608
–618
.10.1016/j.fss.2009.10.0134.
Huang
, C.
, and Huang
, T.
, 2007
, “Dynamics of a Class of Cohen-Grossberg Neural Networks With Time-Varying Delays
,” Nonlinear Anal.: Real World Appl.
, 8
(1
), pp. 40
–52
.10.1016/j.nonrwa.2005.04.0085.
Lien
, C.
, Yu
, K.
, Lin
, Y.
, Chang
, H.
, and Chung
, Y.
, 2011
, “Stability Analysis for Cohen-Grossberg Neural Networks With Time-Varying Delays Via LMI Approach
,” Expert Syst. Appl.
, 38
(5
), pp. 6360
–6367
.10.1016/j.eswa.2010.11.1036.
Lin
, W.
, 2009
, “Dynamics Asymptotic Behavior of Periodic Cohen-Grossberg Neural Networks With Delays
,” Neural Comput.
, 21
(12
), pp. 3444
–3459
.10.1162/neco.2009.08-08-8407.
Oliveira
, J. J.
, 2011
, “Global Stability of a Cohen-Grossberg Neural Network With Both Time-Varying and Continuous Distributed Delays
,” Nonlinear Anal.: Real World Appl.
, 12
(5
), pp. 2861
–2870
.10.1016/j.nonrwa.2011.04.0128.
Yang
, T.
, Yang
, L.
, Wu
, C.
, and Chua
, L. O.
, 1996
, “Fuzzy Cellular Neural Networks: Theory
,” Proceedings of IEEE International Workshop on Cellular Neural Networks and Applications
, pp. 181
–186
.9.
Yang
, T.
, Yang
, L.
, Wu
, C.
, and Chua
, L. O.
, 1996
, “Fuzzy Cellular Neural Networks: Applications
,” Proceedings of IEEE International Workshop on Cellular Neural Networks and Applications
, pp. 225
–230
.10.
He
, D.
, and Xu
, D.
, 2008
, “Attracting and Invariant Sets of Fuzzy Cohen-Grossberg Neural Networks With Time-Varying Delays
,” Phys. Lett. A
, 372
(47
), pp. 7057
–7062
.10.1016/j.physleta.2008.10.03511.
Huang
, T.
, 2011
, “Robust Stability of Delayed Fuzzy Cohen-Grossberg Neural Networks
,” Comput. Math. Appl.
, 61
(8
), pp. 2247
–2250
.10.1016/j.camwa.2010.09.03712.
Kim
, Y.
, Zhang
, H.
, Zhang
, X.
, and Cui
, L.
, 2009
, “Novel Criteria on Global Exponential Stability of Fuzzy Cohen-Grossberg Neural Networks With Time-Varying Delay
,” Chinese Control and Decision Conference
, pp. 2986
–2991
.13.
Li
, C.
, Li
, Y.
, and Ye
, Y.
, 2010
, “Exponential Stability of Fuzzy Cohen-Grossberg Neural Networks With Time Delays and Impulsive Effects
,” Commun. Nonlinear Sci. Numer. Simul.
, 15
(11
), pp. 3599
–3606
.10.1016/j.cnsns.2010.01.00114.
Song
, Q.
, and Cao
, J.
, 2007
, “Impulsive Effects on Stability of Fuzzy Cohen-Grossberg Neural Networks With Time-Varying Delays
,” IEEE Trans. Syst., Man, Cybern., Part B: Cybern.
, 37
(3
), pp. 733
–741
.10.1109/TSMCB.2006.88795115.
Ott
, E.
, Grebogi
, C.
, and Yorke
, J. A.
, 1990
, “Controlling Chaos
,” Phys. Rev. Lett.
, 64
, pp. 1196
–1199
.10.1103/PhysRevLett.64.119616.
Pecora
, L. M.
, and Carroll
, T. L.
, 1990
, “Synchronization in Chaotic Systems
,” Phys. Rev. Lett.
, 64
, pp. 821
–824
.10.1103/PhysRevLett.64.82117.
Bouvrie
, J.
, and Slotine
, J. J.
, 2011
, “Synchronization and Redundancy: Implications for Robustness of Neural Learning and Decision Making
,” Neural Comput.
, 23
(11
), pp. 2915
–2941
.10.1162/NECO_a_0018318.
Karimi
, H. R.
, and Gao
, H.
, 2010
, “New Delay-Dependent Exponential H∞ Synchronization for Uncertain Neural Networks With Mixed Time Delays
,” IEEE Trans. Syst., Man, Cybern., Part B: Cybern.
, 40
(1
), pp. 173
–185
.10.1109/TSMCB.2009.202440819.
Meda-Campana
, J. A.
, Castillo-Toledo
, B.
, and Chen
, G.
, 2009
, “Synchronization of Chaotic Systems From a Fuzzy Regulation Approach
,” Fuzzy Sets Syst.
, 160
(19
), pp. 2860
–2875
.10.1016/j.fss.2008.12.00620.
Dzhunusov
, I. A.
, and Fradkov
, A. L.
, 2009
, “Adaptive Synchronization of a Network of Interconnected Nonlinear Lur’e Systems
,” Autom. Remote Control
, 70
(7
), pp. 1190
–1205
.10.1134/S000511790907010821.
Voegtlin
, T.
, 2009
, “Adaptive Synchronization of Activities in a Recurrent Network
,” Neural Comput.
, 21
(6
), pp. 1749
–1775
.10.1162/neco.2009.02-08-70822.
Heydari
, M.
, Salarieh
, H.
, and Behzad
, M.
, 2011
, “Stochastic Chaos Synchronization Using Unscented Kalman-Bucy Filter and Sliding Mode Control
,” Math. Comput. Simul.
, 81
(9
), pp. 1770
–1784
.10.1016/j.matcom.2011.01.01323.
Lin
, T.
, and Lee
, T.
, 2011
, “Chaos Synchronization of Uncertain Fractional-Order Chaotic Systems With Time Delay Based on Adaptive Fuzzy Sliding Mode Control
,” IEEE Trans. Fuzzy Syst.
, 19
(4
), pp. 623
–635
.10.1109/TFUZZ.2011.212748224.
Hu
, C.
, Jiang
, H.
, and Teng
, Z.
, 2010
, “Impulsive Control and Synchronization for Delayed Neural Networks With Reaction-Diffusion Terms
,” IEEE Trans. Neural Networks
, 21
, pp. 67
–81
.10.1109/TNN.2009.203431825.
Khadra
, A.
, Liu
, X.
, and Shen
, X.
, 2005
, “Impulsive Control and Synchronization of Spatiotemporal Chaos
,” Chaos, Solitons Fractals
, 26
(2
), pp. 615
–636
.10.1016/j.chaos.2004.01.02026.
Zhang
, H.
, Ma
, T.
, Huang
, G.
, and Wang
, Z.
, 2010
, “Robust Global Exponential Synchronization of Uncertain Chaotic Delayed Neural Networks Via Dual-Stage Impulsive Control
,” IEEE Trans. Syst., Man, Cybern., Part B: Cybern.
, 40
(3
), pp. 831
–844
.10.1109/TSMCB.2009.203050627.
Njah
, A. N.
, 2010
, “Tracking Control and Synchronization of the New Hyperchaotic Liu System Via Backstepping Techniques
,” Nonlinear Dyn.
, 61
(1–2
), pp. 1
–9
.10.1007/s11071-009-9626-528.
Liu
, X.
, and Chen
, T.
, 2011
, “Cluster Synchronization in Directed Networks Via Intermittent Pinning Control
,” IEEE Trans. Neural Networks
, 22
(7
), pp. 1009
–1020
.10.1109/TNN.2011.217676929.
Wang
, Z.
, Huang
, L.
, Wang
, Y.
, and Zuo
, Y.
, 2010
, “Synchronization Analysis of Networks With Both Delayed and Non-Delayed Couplings Via Adaptive Pinning Control Method
,” Commun. Nonlinear Sci. Numer. Simul.
, 15
(12
), pp. 4202
–4208
.10.1016/j.cnsns.2010.02.00130.
Li
, N.
, Zhang
, Y.
, Hu
, J.
, and Nie
, Z.
, 2011
, “Synchronization for General Complex Dynamical Networks With Sampled-Data
,” Neurocomputing
, 74
(5
), pp. 805
–811
.10.1016/j.neucom.2010.11.00731.
Zhang
, C.
, He
, Y.
, and Wu
, M.
, 2010
, “Exponential Synchronization of Neural Networks With Time-Varying Mixed Delays and Sampled-Data
,” Neurocomputing
, 74
(1–3
), pp. 265
–273
.10.1016/j.neucom.2010.03.02032.
Cai
, S.
, Hao
, J.
, and Liu
, Z.
, 2011
, “Exponential Synchronization of Chaotic Systems With Time-Varying Delays and Parameter Mismatches Via Intermittent Control
,” Chaos
, 21
, p. 023112
.10.1063/1.354179733.
Wang
, Y.
, Hao
, J.
, and Zuo
, Z.
, 2010
, “A New Method for Exponential Synchronization of Chaotic Delayed Systems Via Intermittent Control
,” Phys. Lett. A
, 374
(19–20
), pp. 2024
–2029
.10.1016/j.physleta.2010.02.06934.
Gan
, Q.
, 2012
, “Exponential Synchronization of Stochastic Cohen-Grossberg Neural Networks With Mixed Time-Varying Delays and Reaction-Diffusion Via Periodically Intermittent Control
,” Neural Networks
, 31
, pp. 12
–21
.10.1016/j.neunet.2012.02.03935.
Hu
, C.
, Yu
, J.
, Jiang
, H.
, and Teng
, Z.
, 2010
, “Exponential Lag Synchronization for Neural Networks With Mixed Delays Via Periodically Intermittent Control
,” Chaos
, 20
, p. 023108
.10.1063/1.339190036.
Hu
, C.
, Yu
, J.
, Jiang
, H.
, and Teng
, Z.
, 2010
, “Exponential Stabilization and Synchronization of Neural Networks With Time-Varying Delays Via Periodically Intermittent Control
,” Nonlinearity
, 23
(10
), pp. 2369
–2391
.10.1088/0951-7715/23/10/00237.
Huang
, Y.
, 2001
, “Resynchronization of Delayed Neural Networks
,” Discrete Contin. Dyn. Syst.
, 7
, pp. 397
–401
.10.3934/dcds.2001.7.39738.
Tang
, Y.
, Wang
, Z.
, and Fang
, J.
, 2011
, “Controller Design for Synchronization of an Array of Delayed Neural Networks Using a Controllable Probabilistic PSO
,” Inf. Sci.
, 181
(20
), pp. 4715
–4732
.10.1016/j.ins.2010.09.02539.
Wang
, Q.
, Shi
, X.
, and Chen
, G.
, 2011
, “Delay-Induced Synchronization Transition in Small-World Hodgkin-Huxley Neuronal Networks With Channel Blocking
,” Discrete Contin. Dyn. Syst., Ser. B
, 16
(2
), pp. 607
–621
.10.3934/dcdsb.2011.16.39340.
Yang
, X.
, and Cao
, J.
, 2009
, “Stochastic Synchronization of Coupled Neural Networks With Intermittent Control
,” Phys. Lett. A
, 373
(36
), pp. 3259
–3272
.10.1016/j.physleta.2009.07.01341.
Yu
, J.
, Hu
, C.
, Jiang
, H.
, and Teng
, Z.
, 2011
, “Exponential Synchronization of Cohen-Grossberg Neural Networks Via Periodically Intermittent Control
,” Neurocomputing
, 74
(10
), pp. 1776
–1782
.10.1016/j.neucom.2011.02.01542.
Zhang
, W.
, Huang
, J.
, and Wei
, P.
, 2011
, “Weak Synchronization of Chaotic Neural Networks With Parameter Mismatch Via Periodically Intermittent Control
,” Appl. Math. Modell.
, 35
(2
), pp. 612
–620
.10.1016/j.apm.2010.07.00943.
Haykin
, S.
, 1994
, Neural Networks
, Prentice-Hall
, Englewood Cliffs, NJ
.44.
Lv
, T.
, and Yan
, P.
, 2010
, “Exponential Synchronization of Delayed Fuzzy Cohen-Grossberg Neural Networks With Reaction Diffusion Term
,” Lect. Notes Comput. Sci.
, 6319
, pp. 57
–63
.10.1007/978-3-642-16530-645.
Zheng
, W.
, and Zhang
, J.
, 2010
, “Stability Analysis of Fuzzy Cohen-Grossberg Neural Networks With Distributed Delays and Reaction-Diffusion Terms
,” Lect. Notes Comput. Sci.
, 6063
, pp. 684
–692
.10.1007/978-3-642-13278-046.
Balasubramaniam
, P.
, and Vidhya
, C.
, 2012
, “Exponential Stability of Stochastic Reaction-Diffusion Uncertain Fuzzy Neural Networks With Mixed Delays and Markovian Jumping Parameters
,” Expert Sys. Appl.
, 39
(3
), pp. 3109
–3115
.10.1016/j.eswa.2011.08.17447.
Yang
, T.
, and Yang
, L.
, 1996
, “The Global Stability of Fuzzy Neural Network
,” IEEE Trans. Circuits. Syst.
, 43
(10
), pp. 880
–883
.10.1109/81.538999Copyright © 2013 by ASME
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