Synchronization in an array of nonlinearly coupled chaotic neural networks with delay coupling

International Journal of Bifurcation and Chaos

Volumn 18, Issue 10, 2008, Pages 3101-3111

  Lu, Jianquan ^a   Ho, Daniel W C ^a   Cao, Jinde ^b  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b SOUTHEAST UNIVERSITY   (China)

Author keywords

Chaotic neural networks; Complex networks; Delay coupling; Synchronization

Indexed keywords

NEURAL NETWORKS; SYNCHRONIZATION;

CHAOTIC NEURAL NETWORK; COMPLEX DYNAMICAL NETWORKS; DELAY COUPLING; DYNAMICAL NETWORKS; FEEDBACK STRENGTH; LYAPUNOV-KRASOVSKII STABILITY THEOREM; NEAREST NEIGHBORS; NONLINEARLY COUPLED;

COMPLEX NETWORKS;

EID: 59049093864     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127408022275     Document Type: Article

References (31)

1. Barabási, A. & Albert, R. [1999] "Emergence of scaling in random networks," Science 286, 509-512.
2. Barahona, M. & Pecora, L. [2002] "Synchronization in small-world systems," Phys. Rev. Lett. 89, 054101,
3. Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. & Zhou, C. [2002] "The synchronization of chaotic systems," Phys. Rep. 366, 1-101.
4. Cao, J. & Ho, D. [2005] "A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach," Chaos Solit. Fract. 24, 1317-1329.
5. Cao, J., Li, P. & Wang, W. [2006] "Global synchronization in arrays of delayed neural networks with constant and delayed coupling," Phys. Lett. A 353, 318-325.
6. Cao, J. & Lu, J. [2006] "Adaptive synchronization of neural networks with or without time-varying delay," Chaos 16, 013133.
7. Chen, G., Zhou, J. Sz Liu, Z. [2004] "Global synchronization of coupled delayed neural networks and applications to chaotic CNN models," Int. J. Bifurcation and Chaos 14, 2229-2240.
8. Chen, M. & Zhou, D. [2006] "Synchronization in uncertain complex networks," Chaos 16, 013101.
9. Hopfield, J. [1984] "Neurons with graded response have collective computational properties like those of twostate neurons," Proc. Nat. Acad. Sci. 81, 3088-3092.
10. Huang, D. [2005] "Simple adaptive-feedback controller for identical chaos synchronization," Phys. Rev. E 71, 037203.
11. Hwang, D., Chavez, M., Am arm, A. & Boccaletti, S. [2005] "Synchronization in complex networks with age ordering," Phys. Rev. Lett. 94, 138701.
12. Huang, W. [2000] "Stabilizing unstable discrete systems by a nonuniformly adaptive adjustment mechanism," Phys. Rev. E 62, 3455-3460.
13. Kocarev, L. & Amato, P. [2005] "Synchronization in power-law networks," Chaos 15, 024101.
14. Krasovskii, N. [1963] Stability of Motion (Stanford University Press).
15. Li, C. & Chen, G. [2004] "Synchronization in general complex dynamical networks with coupling delays," Physica A: Statist. Mech. Appl. 343, 263-278.
16. Li, X., Wang, X. & Chen, G. [2004] "Pinning a complex dynamical network to its equilibrium," IEEE Trans. Circuits Syst.-I 51, 2074-2087.
17. Lu, H. [2002] "Chaotic attractors in delayed neural networks," Phys. Lett. A 298, 109-116.
18. Lu, J. & Cao, J. [2005] "Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters," Chaos 15, 043901.
19. Lü, J. & Chen, G. [2005] "A time-varying complex dynamical network model and its controlled synchronization criteria," IEEE Trans. Autom. Contr. 50, 841-846.
20. Lu, J., He, J., Cao, J. & Gao, Z. [2006] "Topology influences performance in the associative memory neural networks," Phys. Lett. A 354, 335-343.
21. Lu, J. & Cao, J. [2007] "Adaptive synchronization in tree-like dynamical networks," Nonlin. Anal: Real World Appl. 8, 1252-1260.
22. Lu, W. & Chen, T. [2004] "Synchronization of coupled connected neural networks with delays," IEEE Trans. Circuits Syst.-I 51, 2491-2503.
23. Perez-Munuzuri, V., Perez-Villar, V. & Chua, L. [1993] "Autowaves for image processing on a twodimensional CNN array of excitable nonlinear circuits: Flat and wrinkled labrinths," IEEE Trans. Circuits Syst.-I 40, 174-181.
24. Pyragas, K. [1998] "Synchronization of coupled timedelay systems: Analytical estimations," Phys. Rev. E 58, 3067-3071.
25. Ramaswamy, R., Sinha, S. & Gupte, N. [1998] "Targeting chaos through adaptive control," Phys. Rev. E 57, 2507-2510.
26. Strogatz, S. [2001] "Exploring complex networks," Nature 410, 268-276.
27. Wang, W. & Cao, J. [2006] "Synchronization in an array of linearly coupled networks with time-varying delay," Physica A: Statist. Mech. Appl. 366, 197-211.
28. Wang, X. [2002] "Complex networks: Topology, dynamics and synchronization," Int. J. Bifurcation and Chaos 12, 885-916.
29. Watts, D. & Strogatz, S. [1998] "Collective dynamics of 'small-world' networks," Nature 393, 440-442.
30. Wu, C. & Chua, L. [1995] "Synchronization in an array of linearly coupled dynamical systems," IEEE Trans. Circuits Syst.-I 42, 430-447.
31. Xu, S., Lam, J., Ho, D. & Zou, Y. [2005] "Novel global asymptotic stability criteria for delayed cellular neural networks," IEEE Trans. Circuits Syst.-II 52, 349-353.