Exponential synchronization of complex delayed dynamical networks with general topology

Physica A: Statistical Mechanics and its Applications

Volumn 387, Issue 2-3, 2008, Pages 643-652

  Liu, Tao ^a   Dimirovski, Georgi M ^b,c   Zhao, Jun ^a  

^a KEY LABORATORY OF INTEGRATED AUTOMATION OF PROCESS INDUSTRY   (China)

^b DOGUS UNIVERSITY   (Turkey)

^c SS CYRIL AND METHODIUS UNIVERSITY   (Macedonia)

Author keywords

Complex dynamical network; Coupling delays; Decentralized control; Directed and weighted network; Exponential synchronization; Lyapunov functional

Indexed keywords

COMPUTER SIMULATION; DECENTRALIZED CONTROL; DELAY CIRCUITS; DYNAMICAL SYSTEMS; LYAPUNOV FUNCTIONS; SYNCHRONIZATION;

COMPLEX DYNAMICAL NETWORKS; COUPLING DELAYS; DIRECTED AND WEIGHTED NETWORKS; EXPONENTIAL SYNCHRONIZATION;

ELECTRIC NETWORK TOPOLOGY;

EID: 36549066802     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2007.09.019     Document Type: Article

References (23)

1. Strogatz S.H. Exploring complex networks. Nature 410 (2001) 268-276
2. Newman M. The structure and functions of complex networks. SIAM Rev. 45 (2003) 167-256
3. Ding M.Z., and Yang Y.M. Stability of synchronous chaos and on-off intermittency in coupled map lattices. Phys. Rev. E 56 4 (1997) 4009-4016
4. Lü J., Yu X., and Chen G. Chaos synchronization of general complex dynamical networks. Physica A 334 (2004) 281-302
5. 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
6. Watts D.J., and Strogatz S.H. Collective dynamical of 'small-world' networks. Nature 393 (1998) 440-442
7. Barabási A.L., and Albert R. Emergence of scaling in random networks. Science 286 (1999) 509-512
8. Barabási A.L., Albert R., and Jeong H. Mean-field theory for scale-free random networks. Physica A 272 (1999) 173-187
9. Wang X.F., and Chen G. Synchronization in small-word dynamical networks. Int. J. Bifur. Chaos 12 1 (2002) 187-192
10. Wang X.F., and Chen G. Synchronization in scale-free dynamical networks: Robustness and fragility. IEEE Trans. Circuits Syst. I 49 1 (2002) 54-62
11. Hong H., Choi M.Y., and Kim B.J. Synchronization on small-world networks. Phys. Rev. E 65 (2002) 026139
12. Barahona M., and Pecora L.M. Synchronization in small-world systems. Phys. Rev. Lett. 89 (2002) 054101
13. Lü J., Yu X., Chen G., and Cheng D. Characterizing the synchronizability of small-world dynamical networks. IEEE Trans. Circuits Syst. I 51 4 (2004) 787-796
14. Li C., and Chen G. Synchronization in general complex dynamical networks with coupling delays. Physica A 343 (2004) 263-278
15. Lü J., and Chen G. A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Trans. Automat. Control 50 6 (2005) 841-846
16. Zhou J., and Chen T. Synchronization in general complex delayed dynamical networks. IEEE Trans. Circuits Syst. I 53 3 (2006) 733-744
17. Gao H., Lam J., and Chen G. New criteria for synchronization stability of general complex dynamical networks with coupling delays. Phys. Lett. A 360 2 (2006) 263-273
18. Xiang L.Y., Liu Z.X., Chen Z.Q., Chen F., and Yuan Z.Z. Pinning control of complex dynamical networks with general topology. Phys. A 379 (2007) 298-306
19. Zhou J., Lu J., and Lü J. Adaptive synchronization of an uncertain complex dynamical network. IEEE Trans. Automat. Control 51 4 (2006) 652-656
20. Li Z., and Chen G. Robust adaptive synchronization of uncertain dynamical networks. Phys. Lett. A 324 (2004) 166-178
21. Li Z., Feng G., and Hill D. Controlling complex dynamical networks with coupling delays to a desired orbit. Phys. Lett. A 359 (2006) 42-46
22. Li D., Lu J., Wu X., and Chen G. Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system. J. Math. Anal. Appl. 323 (2006) 844-853
23. Lü J., Chen G., Cheng D., and Celikovsky S. Bridge the gap between the Lorenz and the Chen system. Int. J. Bifur. Chaos 12 12 (2002) 2917-2926