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pth Moment Exponential Synchronization of a Class of Chaotic Neural Networks with Mixed Delays

Authors :
Liu, Z.
Lü, S.
Zhong, S.
Mao Ye
Source :
Scopus-Elsevier
Publication Year :
2009
Publisher :
Zenodo, 2009.

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.<br />{"references":["T .L. Carroll, L .M. Pecora. Synchronization in chaotic systems. Phys.\nRev. Lett, 1990, 64: 821-824.","T .L. Carroll, L .M. Pecora. Synchronizing chaotic circuits. IEEE Trans.\nCirc. Syst, 1991, 38: 453-456.","T .Li, S .M. Fei, K .J. Zhang. Synchronization control of recurrent neural\nnetworks with distributed delays. Physica A, 2008, 387: 982-996.","T .Liu, G .M. Dimirovskib, J .Zhao. Exponential synchronization of\ncomplex delayed dynamical networks with general topology. Phys. Lett.\nA, 2008, 387: 643-652.","X .Lou, B .Cui. Synchronization of neural networks based on parameter\nidentification and via output or state coupling, Journal of Computational\nand Applied Mathematics (2007), doi:10.1016/j.cam.2007.11.015.","S .Li. et al., Adaptive exponential synchronization of delayed ..., Chaos,\nSolitons, Fractals (2007), doi:10.1016/j.chaos.2007.08.047.","T . Li, S .M. Fei, Q .Zhu, S .Song. Exponential synchronization of\nchaotic neural networks with mixed delays, Neurocomputing (2008),\ndoi:10.1016/j.neucom.2007.12.029.","J .Yan, J .Lin, M .Hung, T .Liao. On the synchronization of neural\nnetworks containing time-varying delays and sector nonlinearity, Phys.\nLett. A, 2007, 361: 70-77.","Y .Dai, Y .Z. Cai, X .M. Xu. Synchronization and Exponential Estimates\nof Complex Networks with Mixed Time-varying Coupling Delays. Int.\nJour. Auto. Comput.,, 2007, 4(1): 100-106.\n[10] Y .Q. Yang, J .D. Cao. Exponential lag synchronization of a class of\nchaotic delayed neural networks with impulsive effects. Physica A, 2007,\n386: 492-502.\n[11] W .Yu, J .D. Cao. Adaptive synchronization and lag synchronization\nof uncertain dynamical system with time delay based on parameter\nidentification. Phys. Lett. A,, 2007, 375: 467-482\n[12] Q .J. Zhang, J .A. Lu. Chaos synchronization of a new chaotic system\nvia nonlinear control. Chaos, Solitons and Fractals, 2008, 37: 175-179\n[13] H .G. Zhang, Y .H. Xie, Z .L. Wang. Adaptive synchronization between\ntwo different chaotic neural networks with time delay. IEEE Transaction\non Neural Networks, 2007, 18: 1841-1845.\n[14] C.T.H. Baker, E. Buckwar. Exponential stability in pth mean of solutions,\nand of convergent Euler-type solutions, of stochastic delay differential\nequations. J. Comput. Appl. Math, 2005, 184: 404-427.\n[15] J .W. Luo. A note on exponential stability in pth mean of solutions of\nstochastic delay differential equations. J. Comput. Appl. Math, 2007, 198:\n143-148.\n[16] Z .G. Yang, D .Y. Xu, L .Xiang. Exponential p-stability of impulsive\nstochastic differential equations with delays. Phys. Lett. A, 2006, 359:\n129-137.\n[17] X .R. Mao. Exponential stability in mean square of neutral stochastic\ndifferential functional equations. Sys. Contr.Lett, 1995, 26: 245-251.\n[18] X .R. Mao. Razumikhin type theorems on exponential stability of neutral\nstochastic functional differential equations. SIAM J. Math. Anal, 1997,\n28(2): 389-401.\n[19] J. Randjelovi'c, S. Jankovi'c. On the pth moment exponential stability\ncriteria of neutral stochastic functional differential equations. J. Math.\nAnal. Appl, 2007, 326: 266-280.\n[20] Y .H. Sun, J .D. Cao. pth moment exponential stability of stochastic\nrecurrent neural networks with time-varying delays. Nonlinear Anal: Real.\nworld. Appl., 2007, 8: 1171-1185.\n[21] L .Wan, J .Sun. Mean square exponential stability of stochastic delayed\nHopfield neural networks. Phys. Lett. A, 2005, 343:306-318.\n[22] C .X. Huang, et al. pth moment stability analysis of stochastic recurrent\nneural networks with time-varying delays. Inf.Sci., 2008, 178: 2194-2203.\n[23] S .J. Wu, D .Han, X .Z. Meng. p-Moment stability of stochastic\ndifferential equations with jumps. J. Comput. Appl. Math, 2004, 152:\n505-519.\n[24] S .J. Wu, X .L. Guo, Y .Zhou. p-moment stability of functional\ndifferential equations with random impulsive. Comput. Math. Appl., 2006,\n52: 1683-1694.\n[25] H .J. Wu, J .T. Sun. p-Moment stability of stochastic differential\nequations with impulsive jump and Markovian switching. Automatica,\n2006, 42: 1753-1759.\n[26] X .R. Mao. Stochastic Differential Equation and Application, Horwood\nPublishing, Chichester, 1997.\n[27] D .Y. Xu,Z .Wei, S. J. Long. Global exponential stability of impulsive\nintegro-differential equation. Nonlinear Analysis, 2006, 64: 2805-2816."]}

Details

Language :
English
Database :
OpenAIRE
Journal :
Scopus-Elsevier
Accession number :
edsair.doi.dedup.....6b886a163406adc1f9d496d508f8cb6e
Full Text :
https://doi.org/10.5281/zenodo.1079284