pth Moment Exponential Synchronization of a Class of Chaotic Neural Networks with Mixed Delays
This paper studies the pth moment exponential synchronization of a class of stochastic neural networks with mixed delays. Based on Lyapunov stability theory, by establishing a new integrodifferential inequality with mixed delays, several sufficient conditions have been derived to ensure the pth moment exponential stability for the error system. The criteria extend and improve some earlier results. One numerical example is presented to illustrate the validity of the main results.
[1] T .L. Carroll, L .M. Pecora. Synchronization in chaotic systems. Phys.
Rev. Lett, 1990, 64: 821-824.
[2] T .L. Carroll, L .M. Pecora. Synchronizing chaotic circuits. IEEE Trans.
Circ. Syst, 1991, 38: 453-456.
[3] T .Li, S .M. Fei, K .J. Zhang. Synchronization control of recurrent neural
networks with distributed delays. Physica A, 2008, 387: 982-996.
[4] T .Liu, G .M. Dimirovskib, J .Zhao. Exponential synchronization of
complex delayed dynamical networks with general topology. Phys. Lett.
A, 2008, 387: 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] S .Li. et al., Adaptive exponential synchronization of delayed ..., Chaos,
Solitons, Fractals (2007), doi:10.1016/j.chaos.2007.08.047.
[7] T . Li, S .M. Fei, Q .Zhu, S .Song. 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, 2007, 361: 70-77.
[9] Y .Dai, Y .Z. Cai, X .M. Xu. Synchronization and Exponential Estimates
of Complex Networks with Mixed Time-varying Coupling Delays. Int.
Jour. Auto. Comput.,, 2007, 4(1): 100-106.
[10] Y .Q. Yang, J .D. Cao. Exponential lag synchronization of a class of
chaotic delayed neural networks with impulsive effects. Physica A, 2007,
386: 492-502.
[11] W .Yu, J .D. Cao. Adaptive synchronization and lag synchronization
of uncertain dynamical system with time delay based on parameter
identification. Phys. Lett. A,, 2007, 375: 467-482
[12] Q .J. Zhang, J .A. Lu. Chaos synchronization of a new chaotic system
via nonlinear control. Chaos, Solitons and Fractals, 2008, 37: 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, 2007, 18: 1841-1845.
[14] C.T.H. Baker, E. Buckwar. Exponential stability in pth mean of solutions,
and of convergent Euler-type solutions, of stochastic delay differential
equations. J. Comput. Appl. Math, 2005, 184: 404-427.
[15] J .W. Luo. A note on exponential stability in pth mean of solutions of
stochastic delay differential equations. J. Comput. Appl. Math, 2007, 198:
143-148.
[16] Z .G. Yang, D .Y. Xu, L .Xiang. Exponential p-stability of impulsive
stochastic differential equations with delays. Phys. Lett. A, 2006, 359:
129-137.
[17] X .R. Mao. Exponential stability in mean square of neutral stochastic
differential functional equations. Sys. Contr.Lett, 1995, 26: 245-251.
[18] X .R. Mao. Razumikhin type theorems on exponential stability of neutral
stochastic functional differential equations. SIAM J. Math. Anal, 1997,
28(2): 389-401.
[19] J. Randjelovi'c, S. Jankovi'c. On the pth moment exponential stability
criteria of neutral stochastic functional differential equations. J. Math.
Anal. Appl, 2007, 326: 266-280.
[20] Y .H. Sun, J .D. Cao. pth moment exponential stability of stochastic
recurrent neural networks with time-varying delays. Nonlinear Anal: Real.
world. Appl., 2007, 8: 1171-1185.
[21] L .Wan, J .Sun. Mean square exponential stability of stochastic delayed
Hopfield neural networks. Phys. Lett. A, 2005, 343:306-318.
[22] C .X. Huang, et al. pth moment stability analysis of stochastic recurrent
neural networks with time-varying delays. Inf.Sci., 2008, 178: 2194-2203.
[23] S .J. Wu, D .Han, X .Z. Meng. p-Moment stability of stochastic
differential equations with jumps. J. Comput. Appl. Math, 2004, 152:
505-519.
[24] S .J. Wu, X .L. Guo, Y .Zhou. p-moment stability of functional
differential equations with random impulsive. Comput. Math. Appl., 2006,
52: 1683-1694.
[25] H .J. Wu, J .T. Sun. p-Moment stability of stochastic differential
equations with impulsive jump and Markovian switching. Automatica,
2006, 42: 1753-1759.
[26] X .R. Mao. Stochastic Differential Equation and Application, Horwood
Publishing, Chichester, 1997.
[27] D .Y. Xu,Z .Wei, S. J. Long. Global exponential stability of impulsive
integro-differential equation. Nonlinear Analysis, 2006, 64: 2805-2816.
[1] T .L. Carroll, L .M. Pecora. Synchronization in chaotic systems. Phys.
Rev. Lett, 1990, 64: 821-824.
[2] T .L. Carroll, L .M. Pecora. Synchronizing chaotic circuits. IEEE Trans.
Circ. Syst, 1991, 38: 453-456.
[3] T .Li, S .M. Fei, K .J. Zhang. Synchronization control of recurrent neural
networks with distributed delays. Physica A, 2008, 387: 982-996.
[4] T .Liu, G .M. Dimirovskib, J .Zhao. Exponential synchronization of
complex delayed dynamical networks with general topology. Phys. Lett.
A, 2008, 387: 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] S .Li. et al., Adaptive exponential synchronization of delayed ..., Chaos,
Solitons, Fractals (2007), doi:10.1016/j.chaos.2007.08.047.
[7] T . Li, S .M. Fei, Q .Zhu, S .Song. 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, 2007, 361: 70-77.
[9] Y .Dai, Y .Z. Cai, X .M. Xu. Synchronization and Exponential Estimates
of Complex Networks with Mixed Time-varying Coupling Delays. Int.
Jour. Auto. Comput.,, 2007, 4(1): 100-106.
[10] Y .Q. Yang, J .D. Cao. Exponential lag synchronization of a class of
chaotic delayed neural networks with impulsive effects. Physica A, 2007,
386: 492-502.
[11] W .Yu, J .D. Cao. Adaptive synchronization and lag synchronization
of uncertain dynamical system with time delay based on parameter
identification. Phys. Lett. A,, 2007, 375: 467-482
[12] Q .J. Zhang, J .A. Lu. Chaos synchronization of a new chaotic system
via nonlinear control. Chaos, Solitons and Fractals, 2008, 37: 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, 2007, 18: 1841-1845.
[14] C.T.H. Baker, E. Buckwar. Exponential stability in pth mean of solutions,
and of convergent Euler-type solutions, of stochastic delay differential
equations. J. Comput. Appl. Math, 2005, 184: 404-427.
[15] J .W. Luo. A note on exponential stability in pth mean of solutions of
stochastic delay differential equations. J. Comput. Appl. Math, 2007, 198:
143-148.
[16] Z .G. Yang, D .Y. Xu, L .Xiang. Exponential p-stability of impulsive
stochastic differential equations with delays. Phys. Lett. A, 2006, 359:
129-137.
[17] X .R. Mao. Exponential stability in mean square of neutral stochastic
differential functional equations. Sys. Contr.Lett, 1995, 26: 245-251.
[18] X .R. Mao. Razumikhin type theorems on exponential stability of neutral
stochastic functional differential equations. SIAM J. Math. Anal, 1997,
28(2): 389-401.
[19] J. Randjelovi'c, S. Jankovi'c. On the pth moment exponential stability
criteria of neutral stochastic functional differential equations. J. Math.
Anal. Appl, 2007, 326: 266-280.
[20] Y .H. Sun, J .D. Cao. pth moment exponential stability of stochastic
recurrent neural networks with time-varying delays. Nonlinear Anal: Real.
world. Appl., 2007, 8: 1171-1185.
[21] L .Wan, J .Sun. Mean square exponential stability of stochastic delayed
Hopfield neural networks. Phys. Lett. A, 2005, 343:306-318.
[22] C .X. Huang, et al. pth moment stability analysis of stochastic recurrent
neural networks with time-varying delays. Inf.Sci., 2008, 178: 2194-2203.
[23] S .J. Wu, D .Han, X .Z. Meng. p-Moment stability of stochastic
differential equations with jumps. J. Comput. Appl. Math, 2004, 152:
505-519.
[24] S .J. Wu, X .L. Guo, Y .Zhou. p-moment stability of functional
differential equations with random impulsive. Comput. Math. Appl., 2006,
52: 1683-1694.
[25] H .J. Wu, J .T. Sun. p-Moment stability of stochastic differential
equations with impulsive jump and Markovian switching. Automatica,
2006, 42: 1753-1759.
[26] X .R. Mao. Stochastic Differential Equation and Application, Horwood
Publishing, Chichester, 1997.
[27] D .Y. Xu,Z .Wei, S. J. Long. Global exponential stability of impulsive
integro-differential equation. Nonlinear Analysis, 2006, 64: 2805-2816.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:61507", author = "Zixin Liu and Shu Lü and Shouming Zhong and Mao Ye", title = "pth Moment Exponential Synchronization of a Class of Chaotic Neural Networks with Mixed Delays", abstract = "This paper studies the pth moment exponential synchronization of a class of stochastic neural networks with mixed delays. Based on Lyapunov stability theory, by establishing a new integrodifferential inequality with mixed delays, several sufficient conditions have been derived to ensure the pth moment exponential stability for the error system. The criteria extend and improve some earlier results. One numerical example is presented to illustrate the validity of the main results.
", keywords = "pth Moment Exponential synchronization, Stochastic, Neural networks, Mixed time delays", volume = "3", number = "9", pages = "733-6", }
