Mean Square Exponential Synchronization of Stochastic Neutral Type Chaotic Neural Networks with Mixed Delay
This paper studies the mean square exponential synchronization problem of a class of stochastic neutral type chaotic neural networks with mixed delay. On the Basis of Lyapunov stability theory, some sufficient conditions ensuring the mean square exponential synchronization of two identical chaotic neural networks are obtained by using stochastic analysis and inequality technique. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. The feedback controller used in this paper is more general than those used in previous literatures. One simulation example is presented to demonstrate the effectiveness of the derived results.
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Lett 64 (1990) 821-824.
[2] T.L. Carroll, L.M. Pecora, Synchronizing chaotic circuits, IEEE Trans.
Circ. Syst 38 (1991) 453-456.
[3] T. Li, S.M. Fei, K.J. Zhang, Synchronization control of recurrent neural
networks with distributed delays, Physica A 387 (2008) 982-996.
[4] T. Liu, G. M. Dimirovskib, J. Zhao, Exponential synchronization of
complex delayed dynamical networks with general topology, Physics
Letters A 387 (2008) 643-652.
[5] X. Lou, B. Cui, Synchronization of neural networks based on parameter
identification and via output or state coupling, Journal of Computational
and Applied Mathematics (2007), doi:10.1016/j.cam.2007.11.015.
[6] Sheng L et al., Adaptive exponential synchronization of delayed ...,
Chaos, Solitons, Fractals (2007), doi:10.1016/j.chaos.2007.08.047.
[7] Tao Li, Shu-Min Fei, Qing Zhu and Shen Cong, Exponential synchronization
of chaotic neural networks with mixed delays, Neurocomputing
(2008), doi:10.1016/j.neucom.2007.12.029.
[8] J. Yan, J. Lin, M. Hung, T. Liao, On the synchronization of neural
networks containing time-varying delays and sector nonlinearity, Phys.
Lett. A 361 (2007) 70-77.
[9] J.J. Yan, J.S. Lin,etc, On the synchronization of neural networks containing
time-varying delays and sector nonlinearity, Physics Letters A 361
(2007) 70-77.
[10] Y.Q. Yang, J.D. Cao, Exponential lag synchronization of a class of
chaotic delayed neural networks with impulsive effects, Physica A 386
(2007) 492-502.
[11] W. Yu, J. Cao, Adaptive synchronization and lag synchronization of
uncertain dynamical system with time delay based on parameter identification,
Phys. A 375 (2007) 467-482.
[12] Q. J, Zhang, J.A. Lu, Chaos synchronization of a new chaotic system
via nonlinear control, Chaos, Solitons and Fractals 37 (2008) 175-179.
[13] H.G. Zhang, Y.H. Xie, Z.L. Wang, Adaptive synchronization between
two different chaotic neural networks with time delay, IEEE Transaction
on Neural Networks 18(2007) 1841-1845.
[1] T.L. Carroll, L.M. Pecora, Synchronization in chaotic systems, Phys. Rev.
Lett 64 (1990) 821-824.
[2] T.L. Carroll, L.M. Pecora, Synchronizing chaotic circuits, IEEE Trans.
Circ. Syst 38 (1991) 453-456.
[3] T. Li, S.M. Fei, K.J. Zhang, Synchronization control of recurrent neural
networks with distributed delays, Physica A 387 (2008) 982-996.
[4] T. Liu, G. M. Dimirovskib, J. Zhao, Exponential synchronization of
complex delayed dynamical networks with general topology, Physics
Letters A 387 (2008) 643-652.
[5] X. Lou, B. Cui, Synchronization of neural networks based on parameter
identification and via output or state coupling, Journal of Computational
and Applied Mathematics (2007), doi:10.1016/j.cam.2007.11.015.
[6] Sheng L et al., Adaptive exponential synchronization of delayed ...,
Chaos, Solitons, Fractals (2007), doi:10.1016/j.chaos.2007.08.047.
[7] Tao Li, Shu-Min Fei, Qing Zhu and Shen Cong, Exponential synchronization
of chaotic neural networks with mixed delays, Neurocomputing
(2008), doi:10.1016/j.neucom.2007.12.029.
[8] J. Yan, J. Lin, M. Hung, T. Liao, On the synchronization of neural
networks containing time-varying delays and sector nonlinearity, Phys.
Lett. A 361 (2007) 70-77.
[9] J.J. Yan, J.S. Lin,etc, On the synchronization of neural networks containing
time-varying delays and sector nonlinearity, Physics Letters A 361
(2007) 70-77.
[10] Y.Q. Yang, J.D. Cao, Exponential lag synchronization of a class of
chaotic delayed neural networks with impulsive effects, Physica A 386
(2007) 492-502.
[11] W. Yu, J. Cao, Adaptive synchronization and lag synchronization of
uncertain dynamical system with time delay based on parameter identification,
Phys. A 375 (2007) 467-482.
[12] Q. J, Zhang, J.A. Lu, Chaos synchronization of a new chaotic system
via nonlinear control, Chaos, Solitons and Fractals 37 (2008) 175-179.
[13] H.G. Zhang, Y.H. Xie, Z.L. Wang, Adaptive synchronization between
two different chaotic neural networks with time delay, IEEE Transaction
on Neural Networks 18(2007) 1841-1845.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:56167", author = "Zixin Liu and Huawei Yang and Fangwei Chen", title = "Mean Square Exponential Synchronization of Stochastic Neutral Type Chaotic Neural Networks with Mixed Delay", abstract = "This paper studies the mean square exponential synchronization problem of a class of stochastic neutral type chaotic neural networks with mixed delay. On the Basis of Lyapunov stability theory, some sufficient conditions ensuring the mean square exponential synchronization of two identical chaotic neural networks are obtained by using stochastic analysis and inequality technique. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. The feedback controller used in this paper is more general than those used in previous literatures. One simulation example is presented to demonstrate the effectiveness of the derived results.
", keywords = "Exponential synchronization, stochastic analysis, chaotic neural networks, neutral type system.", volume = "5", number = "8", pages = "1266-7", }
