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

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.1983.6313075
2.
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.2005.04.095
3.
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.2009.10.013
4.
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.2005.04.008
5.
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.2010.11.103
6.
Lin
,
W.
,
2009
, “
Dynamics Asymptotic Behavior of Periodic Cohen-Grossberg Neural Networks With Delays
,”
Neural Comput.
,
21
(
12
), pp.
3444
3459
.10.1162/neco.2009.08-08-840
7.
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.2011.04.012
8.
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.2008.10.035
11.
Huang
,
T.
,
2011
, “
Robust Stability of Delayed Fuzzy Cohen-Grossberg Neural Networks
,”
Comput. Math. Appl.
,
61
(
8
), pp.
2247
2250
.10.1016/j.camwa.2010.09.037
12.
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.2010.01.001
14.
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.2006.887951
15.
Ott
,
E.
,
Grebogi
,
C.
, and
Yorke
,
J. A.
,
1990
, “
Controlling Chaos
,”
Phys. Rev. Lett.
,
64
, pp.
1196
1199
.10.1103/PhysRevLett.64.1196
16.
Pecora
,
L. M.
, and
Carroll
,
T. L.
,
1990
, “
Synchronization in Chaotic Systems
,”
Phys. Rev. Lett.
,
64
, pp.
821
824
.10.1103/PhysRevLett.64.821
17.
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_00183
18.
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.2009.2024408
19.
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.2008.12.006
20.
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/S0005117909070108
21.
Voegtlin
,
T.
,
2009
, “
Adaptive Synchronization of Activities in a Recurrent Network
,”
Neural Comput.
,
21
(
6
), pp.
1749
1775
.10.1162/neco.2009.02-08-708
22.
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.2011.01.013
23.
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.2011.2127482
24.
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.2009.2034318
25.
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.2004.01.020
26.
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.2009.2030506
27.
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/s11071-009-9626-5
28.
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.2011.2176769
29.
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.2010.02.001
30.
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.2010.11.007
31.
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.2010.03.020
32.
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
.10.1063/1.3541797
33.
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.2010.02.069
34.
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.2012.02.039
35.
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
.10.1063/1.3391900
36.
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
.10.1088/0951-7715/23/10/002
37.
Huang
,
Y.
,
2001
, “
Resynchronization of Delayed Neural Networks
,”
Discrete Contin. Dyn. Syst.
,
7
, pp.
397
401
.10.3934/dcds.2001.7.397
38.
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.2010.09.025
39.
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.2011.16.393
40.
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.2009.07.013
41.
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.2011.02.015
42.
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.2010.07.009
43.
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
.10.1007/978-3-642-16530-6
45.
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
.10.1007/978-3-642-13278-0
46.
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.2011.08.174
47.
Yang
,
T.
, and
Yang
,
L.
,
1996
, “
The Global Stability of Fuzzy Neural Network
,”
IEEE Trans. Circuits. Syst.
,
43
(
10
), pp.
880
883
.10.1109/81.538999
You do not currently have access to this content.