Some Simple Synchronization Criteria for Complex Dynamical Networks

IEEE Transactions on Circuits and Systems II: Express Briefs

Volumn 53, Issue 11, 2006, Pages 1185-1189

  Chen, Maoyin ^a  

^a INSTITUTE OF PROCESS ENGINEERING   (China)

Author keywords

Complex dynamical networks; matrix measure; synchronization

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; LARGE SCALE SYSTEMS; MATRIX ALGEBRA;

COMPLEX DYNAMICAL NETWORKS; MATRIX MEASURE; NONZERO EIGENVALUE;

SYNCHRONIZATION;

EID: 34547142768     PISSN: 15497747     EISSN: 15583791     Source Type: Journal    
DOI: 10.1109/TCSII.2006.882363     Document Type: Article

References (25)

1. L. M. Pecora and T. L. Carroll, “Master stability functions for synchronized coupled systems,” Phys. Rev. Lett., vol. 80, no. 10, p. 2109, Mar. 1998.
2. M. Barahona and L. M. Pecora, “Synchronization in small-world systems,” Phys. Rev. Lett., vol. 89, no. 5, p. 054101, Jul. 2002.
3. L. Kocarev and P. Amato, “Synchronization in power-law networks,” Chaos, vol. 15, no. 2, p. 024101, Jun. 2005.
4. X. F.Wang and G. Chen, “Synchronization in scale-free dynamical networks: Robustness and fragility,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 1, pp. 54–62, Jan. 2002.
5. X. Li and G. Chen, “Synchronization and desynchronization of complex dynamical network: An engineering viewpoint,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 50, no. 11, pp. 1381–1390, Nov. 2003.
6. J. Lü, X. Yu, and G. Chen et al., “Characterizing the synchronizability of small-world dynamical networks,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 51, no. 4, pp. 787–796, Apr. 2004.
7. G. Rangarajan and M. Ding, “Stability of synchronized chaos in coupled dynamical systems,” Phys. Lett. A, vol. 296, no. 1/5, pp. 204–209, 2002.
8. J. Lü, X. Yu, and G. Chen, “Chaos synchronization of general complex dynamical networks,” Physica A, vol. 334, no. 1/2, pp. 281–302, Mar. 2004.
9. J. Fan and X. Wang, “On synchronization in scale-free dynamical networks,” Physica A, vol. 349, no. 3/4, pp. 443–451, Apr. 2005.
10. M. Chen and D. Zhou, “Synchronization in uncertain complex networks,” Chaos, vol. 16, no. 1, p. 013101, Mar. 2006.
11. C. W. Wu, “Synchronization in arrays of coupled nonlinear systems: Passivity, circle criterion, and observer design,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 48, no. 10, pp. 1257–1261, Oct. 2001.
12. M. Chavez, D.-H. Hwang, and A. Amann et al., “Synchronization is enhanced in weighted complex networks,” Phys. Rev. Lett., vol. 94, no. 21, p. 218701, Jun. 2005.
13. J. F. Heagy, T. L. Carroll, and L. M. Pecora, “Synchronous chaos in coupled oscillator systems,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 50, pp. 1874–1885, 1994.
14. D.-U. Huang, M. Chavez, and A. Amann, “Synchronization in complex networks with age ordering,” Phys. Rev. Lett., vol. 94, no. 13, p. 138701, Apr. 2005.
15. P. M. Gade and C. K. Hu, “Synchronous chaos in coupled map lattices with small-world interactions,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 62, no. 5, pp. 6409–6413, Nov. 2000.
16. J. Lü and G. Chen, “Atime-varying complex dynamical network model and its controlled synchronization criteria,” IEEE. Trans. Autom. Control, vol. 50, no. 6, pp. 841–846, Jun. 2005.
17. Y. Chen, G. Rangarajan, and M. Ding, “General stability analysis of synchronized dynamics in coupled systems,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 67, no. 2, p. 026209, Feb. 2003.
18. J. Jost and M. P. Joy, “Spectral properties and synchronization in coupled map lattices,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 65, no. 1, p. 016201, Jan. 2001.
19. W. Lu and T. Chen, “Synchronization of coupled connected neural networks with delays,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 51, no. 12, pp. 2491–2503, Dec. 2004.
20. J. Zhou and T. Chen, “Synchronization in general complex delayed dynamical networks,” IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 53, no. 3, pp. 733–744, Mar. 2006.
21. J. T. Sun and Y. P. Zhang, “Some simple global synchronization criterions for coupled time-varying chaotic systems,” Chaos, Solitons and Fractals, vol. 19, no. 1, pp. 93–98, Jan. 2004.
22. Y. P. Zhang and J. T. Sun, “Chaotic synchronization and anti-synchronization based on suitable separation,” Phys. Lett. A, vol. 330, no. 1, pp. 442–447, Jan. 2004.
23. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1985.
24. G. H. Gene and C. F. Loan, Matrix Computations. London, U.K.: John Hopkins Univ. Press, 1989.
25. G. Leonov, A. Bunin, and N. Koksch, “Attractor localization of the Lorenz system,” Zeitschrift fur Angewandte Mathematik und Mechanik, vol. 67, no. 12, pp. 649–656, 1987.