Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling

Physica A: Statistical Mechanics and its Applications

Volumn 381, Issue 1-2, 2007, Pages 82-92

  Liu, Xiwei ^a   Chen, Tianping ^a  

^a FUDAN UNIVERSITY   (China)

Author keywords

Delayed coupling; Dynamical networks; Nonlinear coupling; Synchronization

Indexed keywords

CHAOS THEORY; LYAPUNOV FUNCTIONS; MATHEMATICAL MODELS; SYNCHRONIZATION;

DELAYED COUPLING; EXPONENTIAL SYNCHRONIZATION; NONLINEAR COUPLED;

NONLINEAR SYSTEMS;

EID: 34249682074     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2007.03.026     Document Type: Article

References (26)

1. Strogatz S.H. Exploring complex networks. Nature 410 (2001) 268-276
2. Newman M.E.J. The structure and function of complex networks. SIAM Rev. 45 (2003) 167-256
3. Erdös P., and Rényi A. On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5 (1960) 17-61
4. Albert R., and Barabsi A.L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74 (2002) 47-97
5. Watts D.J., and Strogatz S.H. Collective dynamics of small-world. Nature 393 (1998) 440-442
6. Barabaśi A.L., and Albert R. Emergence of scaling in random networks. Science 286 (1999) 509-512
7. Pikovsky A.S., Rosenblum M.G., and Kurths J. Synchronization. A Universal Concept in Nonlinear Sciences (2001), Cambridge University Press, Cambridge, England
8. 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
9. Wang X.F., and Chen G. Synchronization small-world dynamical networks. Int. J. Bifur. Chaos 12 1 (2002) 187-192
10. Mirollo R.E., and Strogatz S.H. Synchronization of pulse-coupled biological oscillators. SIAM J. Appl. Math. 50 6 (1990) 1645-1662
11. Yang T., and Chua L.O. Impulsive control and synchronization of nonlinear dynamical systems and application to secure communication. Int. J. Bifur. Chaos 7 3 (1997) 645-664
12. Pecora L.M., and Carroll T.L. Master stability functions for synchronized coupled systems. Phys. Rev. Lett. 80 10 (1998) 2109-2112
13. C.W. Wu, L.O. Chua, Synchronization in an array of linearly coupled dynamical systems, IEEE Trans. Circuits Syst.-1, 42(8), pp. 430-447, 1995.
14. Lu W.L., and Chen T.P. Synchronization of coupled connected neural networks with delays. IEEE Trans. Circuits Syst.-I 51 12 (2004) 2491-2503
15. Lu W.L., and Chen T.P. New approach to synchronization analysis of linearly coupled ordinary differential systems. Physica D 213 (2006) 214-230
16. Li C.G., and Chen G.R. Synchronization in general complex dynamical networks with coupling delays. Physica A 343 (2004) 263-278
17. Zhou J., and Chen T.P. Synchronization in general complex delayed dynamical networks. IEEE Trans. Circuits Syst.-I 53 3 (2006) 733-745
18. Wang Q.Y., Chen G.R., Lu Q.S., and Hao F. Novel criteria of synchronization stability in complex networks with coupling delays. Physica A 378 (2007) 527-536
19. Wu C.W. Synchronization in arrays of coupled nonlinear systems with delay and nonreciprocal time-varying coupling. IEEE Trans. Circuits Syst.-II 52 5 (2005) 282-286
20. Cao J.D., Li P., and Wang W.W. Global synchronization in arrays of delayed neural networks with constant and delayed coupling. Phys. Lett. A 353 (2006) 318-325
21. Lu W.L., Chen T.P., and Chen G.R. Synchronization analysis of linearly coupled systems described by differential equations with a coupling delay. Physica D 221 (2006) 118-134
22. Vasconcelos D.B., Viana R.L., Lopes S.R., Batista A.M., and Pinto S.E.d.S. Spatial correlations and synchronization in coupled map lattices with long-range interactions. Physica A 343 (2004) 201-218
23. Li C.G., Li S.W., Liao X.F., and Yu J.B. Synchronization in coupled map lattices with small-world delayed interactions. Physica A 335 (2004) 365-370
24. Lind P.G., Nunes A., and Gallas JasonA.C. Impact of bistability in the synchronization of chaotic maps with delayed coupling and complex topologies. Physica A 371 (2006) 100-103
25. T.P. Chen, Z.M. Zhu, Exponential synchronization of nonlinear coupled dynamical networks, Int. J. Bifur. Chaos, in press.
26. Matsumoto T., Chua L.O., and Ayaki K. Reality of chaos in the double scroll circuit: a computer-assisted proof. IEEE Trans.Circuit Syst.-I 35 7 (1988) 909-925