Adaptive synchronization of stochastic neural networks with mixed time delays and reaction-diffusion terms

Nonlinear Dynamics

Volumn 69, Issue 4, 2012, Pages 2207-2219

  Gan, Qintao ^a  

^a MECHANICAL ENGINEERING COLLEGE   (China)

Author keywords

Adaptive control; Exponential synchronization; Mixed time delays; Reaction diffusion; Stochastic neural networks

Indexed keywords

ADAPTIVE CONTROL; ADAPTIVE CONTROLLERS; ADAPTIVE SYNCHRONIZATIONS; CHAOTIC NEURAL NETWORK; CONSTANT DELAYS; EXPONENTIAL SYNCHRONIZATION; EXTENSIVE SIMULATIONS; LYAPUNOV-KRASOVSKII FUNCTIONALS; MEAN SQUARE; REACTION DIFFUSION; REACTION-DIFFUSION TERMS; STOCHASTIC ANALYSIS; STOCHASTIC NEURAL NETWORK; TIME-VARYING DELAY;

ADAPTIVE CONTROL SYSTEMS; DIFFUSION IN LIQUIDS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; NEURAL NETWORKS; STOCHASTIC SYSTEMS; SYNCHRONIZATION; TIME VARYING CONTROL SYSTEMS;

TIME DELAY;

EID: 84866090476     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-012-0420-4     Document Type: Article

References (65)

1. Balasubramaniam, P., Vembarasan, V., Rakkiyappan, R.: Leakage delays in T-S fuzzy cellular neural networks. Neural Process. Lett. 33, 111-136 (2011)
2. Balasubramaniam, P., Nagamani, G., Rakkiyappan, R.: Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term. Commun. Nonlinear Sci. Numer. Simul. 16, 4422-4437 (2011)
3. Barrón, M.A., Sen, M.: Synchronization of four coupled van der Pol oscillators. Nonlinear Dyn. 56, 357-367 (2009)
4. Batista, C.A.S., Lopes, S.R., Viana, R.L., Batista, A.M.: Delayed feedback control of bursting synchronization in a scale-free neuronal network. Neural Netw. 23, 114-124 (2010)
5. Bowong, S.: Adaptive synchronization between two different chaotic dynamical systems. Commun. Nonlinear Sci. Numer. Simul. 12, 976-985 (2007) (Pubitemid 46223850)
6. Bowong, S., Kakmeni, F.M.M.: Synchronization of uncertain chaotic systems via backstepping approach. Chaos Solitons Fractals 21, 999-1011 (2004)
7. Cai, S., Hao, J., Liu, Z.: Exponential synchronization of chaotic systems with time-varying delays and parameter mismatches via intermittent control. Chaos 21, 023112 (2011)
8. Cui, B., Lou, X.: Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control. Chaos Solitons Fractals 39, 288-294 (2009)
9. Gan, Q., Xu, R., Yang, P.: Stability analysis of stochastic fuzzy cellular neural networks with time-varying delays and reaction-diffusion terms. Neural Process. Lett. 32, 45-57 (2010)
10. Gan, Q., Xu, R., Yang, P.: Exponential synchronization of stochastic fuzzy cellular neural networks with time delay in the leakage term and reaction-diffusion. Commun. Nonlinear Sci. Numer. Simul. 17, 1862-1870 (2012)
11. Gao, X., Zhong, S., Gao, F.: Exponential synchronization of neural networks with time-varying delays. Nonlinear Anal. TMA 71, 2003-2011 (2009)
12. Ghosh, D., Chowdhury, A.R.: Nonlinear observer-based impulsive synchronization in chaotic systems with multiple attractors. Nonlinear Dyn. 60, 607-613 (2010)
13. Gopalsamy, K.: Stability and Oscillations in Delay Differential Equations of Population Dynamics. Kluwer Academic, Dordrecht (1992)
14. Gopalsamy, K.: Leakage delays in BAM. J. Math. Anal. Appl. 325, 1117-1132 (2007) (Pubitemid 44615832)
15. Grzybowski, J.M.V., Rafikov, M., Balthazar, J.M.: Synchronization of the unified chaotic system and application in secure communication. Commun. Nonlinear Sci. Numer. Simul. 14, 2793-2806 (2009)
16. Gu, K.: An integral inequality in the stability problem of time-delay system. In: Proceedings of 39th IEEE Conference on Decision and Control, December 2000, Sydney, Australia, pp. 2805-2810 (2000) (Pubitemid 32528463)
17. Guo,W.: Lag synchronization of complex networks via pinning control. Nonlinear Anal.: Real World Appl. 12, 2579-2585 (2011)
18. Haykin, S.: Neural Networks. Prentice Hall, New York (1994)
19. He, H., Tu, J.: Algebraic condition of synchronization for multiple time-delayed chaotic Hopfield neural networks. Neural Comput. Appl. 19, 543-548 (2010)
20. Hua, M., Liu, X., Deng, F., Fei, J.: New results on robust exponential stability of uncertain stochastic neural networks with mixed time-varying delays. Neural Process. Lett. 32, 219-233 (2010)
21. Huang, T., Li, C.: Chaotic synchronization by the intermittent feedback method. J. Comput. Appl. Math. 234, 1097-1104 (2010)
22. Ji, D.H., Lee, D.W., Koo, J.H., Won, S.C., Lee, S.M., Park, J.H.: Synchronization of neutral complex dynamical networks with coupling time-varying delays. Nonlinear Dyn. 65, 349-358 (2011)
23. Ji, D.H., Park, J.H., Yoo, W.J., Won, S.C., Lee, S.M.: Synchronization criterion for Lur'e type complex dynamical networks with time-varying delay. Phys. Lett. A 374, 1218-1227 (2010)
24. Kong, C., Chen, S.: Synchronization of noise-perturbed generalized Lorenz system by sliding mode control. Chin. Phys. Soc. 18, 91-97 (2009)
25. Li, C., Yang, S.: Synchronization in delayed Cohen-Grossberg neural networks with bounded external inputs. IMA J. Appl. Math. 74, 178-200 (2009)
26. Li, N., Zhang, Y., Hu, J., Nie, Z.: Synchronization for general complex dynamical networks with sampled-data. Neurocomputing 74, 805-811 (2011)
27. Li, T., Song, A., Fei, S., Fei, J.: Robust stability of stochastic Cohen-Grossberg neural networks with mixed timevarying delays. Neurocomputing 73, 542-551 (2009)
28. Li, X., Rakkiyappan, R., Balasubramaniam, P.: Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations. J. Franklin Inst. 348, 135-155 (2011)
29. Li, Z., Xu, R.: Global asymptotic stability of stochastic reaction-diffusion neural networks with time delays in the leakage terms. Commun. Nonlinear Sci. Numer. Simul. 17, 1681-1689 (2012)
30. Lin, W., He, Y.: Complete synchronization of the noiseperturbed Chua's circuits. Chaos 15, 023705 (2005)
31. Loría, A.: Master-slave synchronization of fourth-order Lü chaotic oscillators via linear output feedback. IEEE Trans. Circuits Syst. II, Express Briefs 57, 213-217 (2010)
32. Lu, J.: Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions. Chaos Solitons Fractals 35, 116-125 (2008) (Pubitemid 47385219)
33. Lv, Y., Lv, W., Sun, J.: Convergence dynamics of stochastic reaction-diffusion recurrent neural networks with continuously distributed delays. Nonlinear Anal.: Real World Appl. 9, 1590-1606 (2008) (Pubitemid 351685799)
34. Ma, Q., Xu, S., Zou, Y., Shi, G.: Synchronization of stochastic chaotic neural networks with reaction-diffusion terms. Nonlinear Dyn. 67, 2183-2196 (2012)
35. Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64, 1196-1199 (1990)
36. Park, J.H.: Adaptive synchronization of a unified chaotic systems with an uncertain parameter. Int. J. Nonlinear Sci. Numer. Simul. 6, 201-206 (2005) (Pubitemid 40588628)
37. Park, J.H.: Synchronization of Genesio chaotic system via backstepping approach. Chaos Solitons Fractals 27, 1369-1375 (2006) (Pubitemid 41329830)
38. Park, J.H.: Adaptive control for modified projective synchronization of a four-dimensional chaotic system with uncertain parameters. J. Comput. Appl. Math. 213, 288-293 (2008)
39. Park, J.H.: Synchronization of cellular neural networks of neutral type via dynamic feedback controller. Chaos Solitons Fractals 42, 1299-1304 (2009)
40. Park, J.H., Ji, D.H., Won, S.C., Lee, S.M.: Adaptive H8 synchronization of unified chaotic systems. Mod. Phys. Lett. B 23, 1157-1169 (2009)
41. Park, J.H., Lee, S.M., Jung, H.Y.: LMI optimization approach to synchronization of stochastic delayed discretetime complex networks. J. Optim. Theory Appl. 143, 357-367 (2009)
42. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821-824 (1990)
43. Salarieh, H., Shahrokhi, M.: Adaptive synchronization of two different chaotic systems with time varying unknown parameters. Chaos Solitons Fractals 37, 125-136 (2008) (Pubitemid 351258308)
44. Sanchez, E.N., Ricalde, L.J.: Chaos control and synchronization, with input saturation, via recurrent neural networks. Neural Netw. 16, 711-717 (2003) (Pubitemid 36794345)
45. Sharma, B.B., Kar, I.N.: Observer-based synchronization scheme for a class of chaotic systems using contraction theory. Nonlinear Dyn. 63, 429-445 (2011)
46. Sheng, L., Yang, H., Lou, X.: Adaptive exponential synchronization of delayed neural networks with reaction-diffusion terms. Chaos Solitons Fractals 40, 930-939 (2009)
47. Shi, G., Ma, Q.: Synchronization of stochastic Markovian jump neural networks with reaction-diffusion terms. Neurocomputing 77, 275-280 (2012)
48. Su, H., Ding, X.: Synchronization in time-discrete delayed chaotic systems. Neurocomputing 73, 478-483 (2009)
49. Tang, Q., Wang, X.: Chaos control and synchronization of cellular neural network with delays based on OPNCL control. Chin. Phys. Lett. 27, 030508 (2010)
50. Wan, L., Zhou, Q.: Exponential stability of stochastic reaction-diffusion Cohen-Grossberg neural networks with delays. Appl. Math. Comput. 206, 818-824 (2008)
51. Wang, J., Lu, J.: Global exponential stability of fuzzy cellular neural networks with delays and reaction-diffusion terms. Chaos Solitons Fractals 38, 878-885 (2008) (Pubitemid 351633036)
52. Wang, L., Zhang, Z., Wang, Y.: Stochastic exponential stability of the delayed reaction-diffusion recurrent neural networks with Markovian jumping parameters. Phys. Lett. A 372, 3201-3209 (2008)
53. Wang, Y., Cao, J.: Synchronization of a class of delayed neural networks with reaction-diffusion terms. Phys. Lett. A 369, 201-211 (2007)
54. Wembe, E.T., Yamapi, R.: Chaos synchronization of resistively coupled duffing systems: numerical and experimental investigations. Commun. Nonlinear Sci. Numer. Simul. 14, 1439-1453 (2009)
55. Xiang, L., Zhu, J.J.H.: On pinning synchronization of general coupled networks. Nonlinear Dyn. 64, 339-348 (2011)
56. Xing, Z., Peng, J., Wang, K.: Exponential synchronization of chaotic neural networks with time delays: A M-matrix approach. Nonlinear Dyn. 62, 867-874 (2010)
57. Yahyazadeh, M., Noei, A.R., Ghaderi, R.: Synchronization of chaotic systems with known and unknown parameters using a modified active sliding mode control. ISA Trans. 50, 262-267 (2011)
58. Yassen, M.T.: Adaptive synchronization of Rossler and Lü systems with fully uncertain parameters. Chaos Solitons Fractals 23, 1527-1536 (2005)
59. Yassen, M.T.: Adaptive chaos control and synchronization for uncertain new chaotic dynamical system. Phys. Lett. A 350, 36-43 (2006) (Pubitemid 43087665)
60. Yu, F., Jiang, H.: Global exponential synchronization of fuzzy cellular neural networks with delays and reaction-diffusion terms. Neurocomputing 74, 509-515 (2011)
61. Yu, Y.: Adaptive synchronization of a unified chaotic system. Int. J. Nonlinear Sci. Numer. Simul. 36, 329-333 (2008) (Pubitemid 47588894)
62. Zhang, C., He, Y., Wu, M.: Exponential synchronization of neural networks with time-varying mixed delays and sampled-data. Neurocomputing 74, 265-273 (2010)
63. Zhang, Q., Zhao, J.: Projective and lag synchronization between general complex networks via impulsive control. Nonlinear Dyn. 67, 2519-2525 (2012)
64. Zhao, B., Deng, F.: Adaptive exponential synchronization of stochastic delay neural networks with reaction-diffusion. Lect. Notes Comput. Sci. 5551, 550-559 (2009)
65. Zhu, Q., Li, X., Yang, X.: Exponential stability for stochastic reaction-diffusion BAM neural networks with timevarying and distributed delays. Appl. Math. Comput. 217, 6078-6091 (2011)