Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays

Communications in Nonlinear Science and Numerical Simulation

Volumn 16, Issue 4, 2011, Pages 2139-2159

  Zhu, Quanxin ^a   Cao, Jinde ^b  

^a NINGBO UNIVERSITY   (China)

^b SOUTHEAST UNIVERSITY   (China)

Author keywords

Adaptive feedback control; Adaptive synchronization; Distributed delay; LaSalle invariant principle; Linear matrix inequality; Stochastic neural network; Time varying delay

Indexed keywords

ADAPTIVE CONTROL SYSTEMS; DYNAMICAL SYSTEMS; FEEDBACK CONTROL; LINEAR MATRIX INEQUALITIES; NEURAL NETWORKS; STOCHASTIC SYSTEMS; SYNCHRONIZATION; TIME DELAY; TIME VARYING CONTROL SYSTEMS; TIME VARYING NETWORKS;

ADAPTIVE FEEDBACK CONTROL; ADAPTIVE SYNCHRONIZATIONS; DELAYED NEURAL NETWORKS; DISTRIBUTED DELAYS; LASALLE INVARIANT PRINCIPLE; LINEAR MATRIX IN EQUALITIES; STOCHASTIC NEURAL NETWORK; STOCHASTICS; SYNCHRONIZATION PROBLEM; TIME-VARYING DELAY;

ASYMPTOTIC STABILITY;

EID: 78049405981     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.08.037     Document Type: Article

References (39)

1. Agiza H.N., Yassen M.T. Synchronization of Rossler and Chen chaotic dynamical systems using active control. Phys Lett A 2001, 278(4):191-197.
2. Boyd S., Ghaoui L., Feron E., Balakrishnan V. Linear matrix inequalities in system and control theory 1994, SIAM, Philadelphia, PA.
3. Carroll T.L., Pecora L.M. Synchronization chaotic circuits. IEEE Trans Circuit Syst 1991, 38(4):453-456.
4. Cao J., Lu J. Adaptive synchronization of neural networks with or without time-varying delays. Chaos 2006, 16(1):013133.
5. Cui B., Lou X. Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control. Chaos Soliton Fract 2009, 39(1):288-294.
6. Fotsin H.B., Woafo P. Adaptive synchronization of a modified and uncertain chaotic Van der Pol-Duffing oscillator based on parameter identification. Chaos Soliton Fract 2005, 24(5):1363-1371.
7. Fotsin H.B., Daafouz J. Adaptive synchronization of uncertain chaotic colpitts oscillators based on parameter identification. Phys Lett A 2005, 339(3-5):304-315.
8. Gu K. An integral inequality in the stability problem of time-delay systems. In: Proceedings of 39th IEEE conference on decision and control, Sydney, Australia; 2000. pp. 2805-10.
9. S. Haykin, Neural Networks, A comprehensive foundation. Prentice Hall, Inc., Upper Saddle River, New Jersey, 1994.
10. He G., Cao Z., Zhu P., Ogura H. Controlling chaos in a chaotic neural network. Neural Networks 2003, 16(8):1195-1200.
11. Heagy J.F., Carroll T.L., Pecora L.M. Experimental and numerical evidence for riddled basins in coupled chaotic systems. Phys Rev Lett 1994, 73(26):3528-3531.
12. Huang D. Simple adaptive-feedback controller for identical chaos synchronization. Phys Rev E 2005, 71:037203.
13. Huang L., Feng R., Wang M. Synchronization of chaotic systems via nonlinear control. Phys Lett A 2004, 320(4):271-275.
14. Kakmeni F., Bowong S., Tchawoua C. Nonlinear adaptive synchronization of a class of chaotic systems. Phys Lett A 2006, 355(1):47-54.
15. Li X., Cao J. Adaptive synchronization for delayed neural networks with stochastic perturbation. J Franklin Inst 2008, 345(7):779-791.
16. Li C., Liao X., Yang X., Huang T. Impulsive stabilization and synchronization of a class of chaotic delay systems. Chaos 2005, 15:023104.
17. Li T., Fei S., Zhu Q., Cong S. Exponential synchronization of chaotic neural networks with mixed delays. Neurocomputing 2008, 71(13-15):3005-3019.
18. Lei Y., Xu W., Zheng H. Synchronization of two chaotic nonlinear gyros using active control. Phys Lett A 2005, 343(1-3):153-158.
19. Lu J., Cao J. Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters. Chaos 2005, 15:043901.
20. Mahboobi S.H., Shahrokhi M., Pishkenari H.N. Observer-based control design for three well-known chaotic systems. Chaos Soliton Fract 2006, 29(2):381-392.
21. Mao X. Stochastic differential equation and application 1997, Horwood Publishing, Chichester.
22. Mao X. A note on the LaSalle-type theorems for stochastic differential delay equations. J Math Anal Appl 2002, 268(1):125-142.
23. Pecora L.M., Carroll T.L. Synchronization in chaotic systems. Phys Rev Lett 1990, 64(8):821-824.
24. Park J.H. Adaptive control for modified projective synchronization of a four-dimensional chaotic system with uncertain parameters. J Comput Appl Math 2008, 213(1):288-293.
25. Park J.H. Synchronization of Genesio chaotic system via backstepping approach. Chaos Soliton Fract 2006, 27(5):1369-1375.
26. Salarieh H., Alasty A. Adaptive synchronization of two chaotic systems with stochastic unknown parameters. Commun Nonlinear Sci Numer Simulat 2009, 14(2):508-519.
27. Sun Y., Cao J., Wang Z. Exponential synchronization of stochastic perturbed chaotic delayed neural networks. Neurocomputing 2007, 70(13-15):2477-2485.
28. Tang Y., Qiu R., Fang J., Miao Q., Xia M. Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays. Phys Lett A 2008, 372(24):4425-4433.
29. Wang C., Su J. A new adaptive variable structure control for chaotic synchronization and secure communication. Chaos Soliton Fract 2004, 20(5):967-977.
30. Wang K., Teng Z., Jiang H. Adaptive synchronization of neural networks with time-varying delay and distributed delay. Physica A 2008, 387(2-3):631-642.
31. Yang Y., Cao J. Exponential lag synchronization of a class of chaotic delayed neural networks with impulsive effects. Physica A 2007, 386(1):492-502.
32. Yu W., Cao J. Synchronization control of stochastic delayed neural networks. Physica A 2007, 373(1):252-260.
33. Zhou J., Chen T., Xiang L. Robust synchronization of delayed neural networks based on adaptive control and parameters identification. Chaos Soliton Fract 2006, 27(4):905-913.
34. Zhu Q., Cao J. Adaptive synchronization of chaotic Cohen-Crossberg neural networks with mixed time delays. Nonlinear Dyn 2010, 61(3):517-534.
35. Zhu Q., Cao J. Stochastic stability of neural networks with both Markovian jump parameters and continuously distributed delays. Discrete Dyn Nat Soc 2009, 2009:20. Article ID 490515.
36. Zhu Q., Cao J. Robust exponential stability of markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans Neural Networks 2010, 21(8):1314-1325.
37. Zhu Q, Cao J. Exponential stability of stochastic neural networks with both Markovian jump parameters and mixed time delays. IEEE Trans Syst Man Cybern B Cybern 2010. in press.
38. Zhu Q., Cao J. Stability analysis for stochastic neural networks of neutral type with both Markovian jump parameters and mixed time delays. Neurocomputing 2010, 73(13-15):2671-2680.
39. Zhu Q., Yang X., Wang H. Stochastically asymptotic stability of delayed recurrent neural networks with both Markovian jump parameters and nonlinear disturbances. J Franklin Inst 2010, 347(2):1489-1510.