A class of Cohen-Grossberg neural networks with discrete delays are investigated in this paper. By using the suitable Lyapunov function, sufficient conditions for adaptive lag synchronization of such systems are obtained. Finally, a numerical example is given to demonstrate the main results.
REFERENCES
1.
L. M.
Pecorn
and T. L.
Carroll
, “Synchronization between linearly coupled chaotic systems
,” Phys. Rev. Lett.
64
(8
), 821
–824
(1990
).2.
B.
Cui
and X.
Lou
, “Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control
,” Chaos, Solitons Fractals
39
, 288
–294
(2009
).3.
C.
Chiu
, W.
Lin
, and C.
Peng
, “Asymptotic synchronization in lattices of coupled nonlinear Lorenz equations
,” Int. J. Bifurcation Chaos
10
, 2717
–2728
(2000
).4.
Y.
Sun
and J.
Cao
, “Adaptive lag synchronization of unknown chaotic delayed neural networks with noise perturbation
,” Phys. Lett. A
364
, 277
–285
(2007
).5.
T.
Yang
and L.
Chua
, “Impulsive control and synchronization of nonlinear dynamical system and application to secure communication
,” Int. J. Bifurcation Chaos
7
, 645
–664
(1997
).6.
H.
Huang
and G.
Feng
, “Synchronization of nonidentical chaotic neural networks with time delays
,” Neural Networks
22
, 869
–874
(2009
).7.
J.
Yu
, C.
Hu
, H.
Jiang
, and Z.
Teng
, “Exponential synchronization of Cohen-Grossberg neural networks via periodically intermittent control
,” Nonlinearity
23
, 2369
–2391
(2010
).8.
M.
Cohen
and S.
Grossberg
, “Absolute stability and global pattern formation and parallel memory storage by competitive neural networks
,” IEEE Trans. Syst. Man Cybern.
Smc-13
, 815
–826
(1983
).http://techlab.bu.edu/files/resources/articles_cns/CohGro1983IEEE.pdf9.
J.
Cao
and Q.
Song
, “Stability in Cohen-Grossberg-type bidirectional associative memory neural networks with time-varying delays
,” Nonlinearity
19
, 1601
–1617
(2006
).10.
H.
Zhao
and L.
Wang
, “Hopf bifurcation in Cohen-Grossberg neural network with distributed delays
,” Nonlinear Anal.: Real World Appl.
8
, 73
–89
(2007
).11.
Q.
Zhou
, L.
Wan
, and J.
Sun
, “Exponential stability of reaction-diffusion generalized Cohen-Grossberg neural networks with time-varying delays
,” Chaos, Solitons Fractals
32
, 1713
–1719
(2007
).12.
Z.
Li
and K.
Li
, “Stability analysis of impulsive Cohen-Grossberg neural networks with distributed delays and reaction-diffusion terms
,” Appl. Math. Modell.
33
, 1337
–1448
(2009
).13.
C.
Li
and S.
Yang
, “Existence and attractivity of periodic solutions to nonautonomous Cohen-Grossberg neural networks with time delays
,” Chaos, Solitons Fractals
41
, 1235
–1244
(2009
).14.
X.
Wang
, Q.
Guo
, and D.
Xu
, “Exponential p-stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays
,” Math. Comput. Simul.
79
, 1698
–1710
(2009
).15.
Q.
Song
and Z.
Wang
, “Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays
,” Physica A
387
, 3314
–3326
(2008
).16.
J.
Cao
, G.
Feng
, and Y.
Wang
, “Multistability and multiperiodicity of delayed Cohen-Grosssberg neural networks with a general class of activation functions
,” Physica D
237
, 1734
–1749
(2008
).17.
J.
Cao
and Y.
Wang
, “Bi-periodicity evoked by periodic external inputs in delayed Cohen-Grossberg-type bidirectional associative memory networks
,” Phys. Scr.
81
, 055803
(2010
).18.
C.
Cheng
, T.
Liao
, and C.
Hwang
, “Exponential synchronization of a class of chaotic neural networks
,” Chaos, Solitons Fractals
24
, 197
–206
(2005
).19.
J.
Chen
, Z.
Wang
, Y.
Liang
, W.
Liao
, and X.
Liao
, “Synchronization of neural networks by decetralized linear-feedback control
,” LNCS
4682
, 157
–163
(2007
).20.
Q.
Zhu
and J.
Cao
, “Adaptive synchronization of chaotic Cohen-Grossberg neural networks with mixed time delays
,” Nonlinear Dyn.
61
, 517
–534
(2010
).21.
Z.
Chen
, “Complete synchronization for impulsive Cohen-Grossberg neural networks with delay under noise perturbation
,” Chaos, Solitons Fractals
42
, 1664
–1669
(2009
).22.
T.
Lv
and P.
Yan
, “Exponential Synchronization of delayed fuzzy Cohen-Grossberg neural networks with reaction diffusion terms
,” LNCS
6319
, 57
–63
(2010
).23.
Q.
Gan
, “Adaptive synchronization of Cohen-Grossberg neural networks with unknown parameters and mixed time-varying delays
,” Commun. Nolinear Sci. Numer. Simul.
17
, 3040
–3049
(2012
).24.
T.
Li
, A.
Song
, and S.
Fei
, “Synchronization control for arrays of coupled discrete-time delayed Cohen-Crossberg neural networks
,” Neurocomouting
74
, 197
–204
(2010
).25.
E. M.
Shahverdiev
, S.
Sivaprakasam
, and K. A.
Shore
, “Lag synchronization in time-delayed systems
,” Phys. Lett. A
292
, 320
–324
(2002
).© 2012 American Institute of Physics.
2012
American Institute of Physics
You do not currently have access to this content.