Adaptive synchronization in an array of chaotic neural networks with mixed delays and jumping stochastically hybrid coupling

Communications in Nonlinear Science and Numerical Simulation

Volumn 14, Issue 9-10, 2009, Pages 3615-3628

  Tang, Yang ^a   Fang, Jian an ^a  

^a DONGHUA UNIVERSITY   (China)

Author keywords

Adaptive synchronization; Chaotic systems; Complex dynamical networks; Markovian jumping parameters; Mixed time varying delays; Stochastically hybrid coupling

Indexed keywords

BROWNIAN MOVEMENT; NEURAL NETWORKS; SMALL-WORLD NETWORKS; STOCHASTIC SYSTEMS; SYNCHRONIZATION; TIME DELAY; TIME VARYING NETWORKS;

ADAPTIVE SYNCHRONIZATIONS; CHAOTIC NEURAL NETWORK; COMPLEX DYNAMICAL NETWORKS; DELAY COUPLING; GENERAL MODEL; HYBRID COUPLINGS; MARKOVIAN JUMPING PARAMETERS; MIXED DELAYS; MIXED TIME-VARYING DELAYS; STOCHASTICALLY HYBRID COUPLING;

CHAOTIC SYSTEMS;

EID: 63449107142     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.02.006     Document Type: Article

References (42)

1. Watts D.J., and Strogatz S.H. Collective dynamical of 'small-world' networks. Nature 393 (1998) 440-442
2. Barabási A.L., and Albert R. Emergence of scaling in random networks. Science 286 (1999) 509-512
3. Strogatz S.H. Exploring complex networks. Nature 410 (2001) 268-276
4. Newman M., and Watts D.J. Renormalization group analysis of the small-world network model. Phys Lett A 263 (1999) 341-346
5. Boccalettia S., Latorab V., Morenod Y., Chavezf M., and Hwanga D.U. Complex networks: Structure and dynamics. Phys Rep 424 (2006) 175-308
6. Luo A.C.J. A theory for synchronization of dynamical systems. Commun Nonlinear Sci Numer Simulat 14 (2009) 1901-1951
7. Luo A.C.J. Global transversality resonance and chaotic dynamics (2008), World Scientific, New Jersey
8. Wu C.W., and Chua L.O. Synchronization in an array of linearly coupled dynamical systems. IEEE Trans Circuits Syst I 42 8 (1995) 430-447
9. Wang X.F., and Chen G.R. Synchronization in small-world dynamical networks. Int J Bifur Chaos 12 1 (2002) 187-192
10. Wang X.F., and Chen G.R. Synchronization in scale-free dynamical networks: robustness and fragility. IEEE Trans Circuits Syst I 49 1 (2002) 1254-1262
11. Lü J., and Chen G.R. A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Trans Automat Control 1950 (2005) 841-846
12. Lü J., Yu X., and Chen G.R. Chaos synchronization of general complex dynamical networks. Physica A 334 (2004) 281-302
13. Lü J., Yu X., Chen G.R., and Cheng D. Characterizing the synchronizability of small-world dynamical networks. IEEE Trans Circuits Syst I 51 4 (2004) 787-796
14. Barahona M., and Pecora L.M. Synchronization in small-world systems. Phys Rev Lett 89 (2002) 054101
15. Tang Y., Wang Z., and Fang J. Pinning control of fractional-order weighted complex networks. Chaos 19 (2009) 013112
16. Wen S., Chen S.H., and Wang C.P. Global synchronization in complex networks consisted of systems with the property of xk-leading asymptotic stability. Phys Lett A 372 17 (2008) 3021-3026
17. Leung H., and Zhu H. A time-varying synchronization of chaotic systems in the presence of system mismatch. Phys Rev E 69 (2004) 02620
18. Kiani A., Fallahi K., Pariz N., and Leung H. A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter. Commun Nonlinear Sci Numer Simulat 14 (2009) 863-879
19. Liu Y., Wang Z., and Liu X. Exponential synchronization of complex networks with Markovian jump and mixed delays. Phys Lett A 372 (2008) 3986-3998
20. Cao J., Wang Z., and Sun Y. Synchronization in an array of linearly stochastically coupled networks with time delays. Physica A 385 (2007) 718-728
21. Cao J., Li P., and Wang W. Global synchronization in arrays of delayed neural networks with constant and delayed coupling. Phys Lett A 353 (2006) 318-325
22. Cao J., Chen G.R., and Li P. Global synchronization in an array of delayed neural networks with hybrid coupling. IEEE Trans Syst Man Cybern B Cybern 38 (2008) 488-498
23. Yu W., Cao J., and Lü J. Global synchronization of linearly hybrid coupled networks with time-varying delay. SIAM J Appl Dyn Syst 7 (2008) 108-133
24. Ruan S., and Filfil R. Dynamics of a two-neuron system with discrete and distributed delays. Physica D 191 (2004) 323-342
25. Wang Z., Liu Y., Li M., and Liu X. Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 17 (2006) 814-820
26. Wang Z., Fang J., and Liu X. Global stability of stochastic high-order neural networks with discrete and distributed delays. Chaos Solitons Fract 36 (2008) 388-396
27. Cao J., and Lu J. Adaptive synchronization of neural networks with or without time-varying delay. Chaos 16 1 (2006) 013133
28. Pecora L.M. Carroll synchronization in chaotic systems. Phys Rev Lett 64 8 (1990) 821-824
29. Tang Y., and Fang J. General methods for modified projective synchronization for hyperchaotic systems with known or unknown parameters. Phys Lett A 372 (2008) 1816-1826
30. Tang Y., Qiu R.H., Fang J., Miao Q., and Xia M. Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays. Phys Lett A 372 (2008) 4425-4433
31. Boccaletti S. The synchronized dynamics of complex systems (2008), Elsevier, Amsterdam
32. Lu H. Chaotic attractors in delayed neural networks. Phys Lett A 298 (2002) 109-116
33. Sompolinsky H., and Crisanti A. Chaos in random neural networks. Phys Rev Lett 61 (1988) 259-262
34. Gilli M. Strange attractors in delayed cellular neural networks. IEEE Trans Circuits Syst I Fundam Theor Appl 40 (1993) 849-853
35. Tino P., Cernansky M., and Benuskova L. Markovian architectural bias of recurrent neural networks. IEEE Trans Neural Netw 15 (2004) 6-15
36. Wang Z., Liu Y., Yu L., and Liu X. Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys Lett A 356 (2006) 346-352
37. Casey M.P. The dynamics of discrete-time computation with application to recurrent neural networks and finite state machine extraction. Neural Comput 8 (1996) 1135-1178
38. Xu S., Chen T., and Lam J. Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays. IEEE Trans Automat Control 48 (2003) 900-907
39. Shen Y., Jiang M., and Liao X. The LaSalle-type theorem for stochastic differential delay equations with Markovian switching. Dynamics of Continuous Discrete and Impulsive Systems-Series A-Mathematical Analysis 13 (2006) 1254-1262
40. Mao X., and Yuan C. Stochastic differential equations with Markovian switching (2006), Imperial College Press
41. Huang D.B. Simple adaptive-feedback controller for identical chaos synchronization. Phys Rev E 71 (2005) 037203
42. Huang D.B. Adaptive-feedback control algorithm. Phys Rev E 73 (2006) 066204