Cluster synchronization and isolated desynchronization in complex networks with symmetries

Nature Communications

Volumn 5, Issue , 2014, Pages

  Pecora, Louis M ^a   Sorrentino, Francesco ^b   Hagerstrom, Aaron M ^c,d   Murphy, Thomas E ^d,e   Roy, Rajarshi ^c,d  

^a NAVAL RESEARCH LABORATORY   (United States)

^b University of New Mexico   (United States)

^c Bldg 142   (United States)

^d The Institute for Research in Electronics and Applied Physics   (United States)

^e UNIVERSITY OF MARYLAND   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CLUSTER ANALYSIS; HETEROGENEITY; NEUROLOGY; TELECOMMUNICATION;

ARTICLE; CELL SYNCHRONIZATION; CORTICAL SYNCHRONIZATION; DECOMPOSITION; LIGHT EMITTING DIODE; NERVE CELL NETWORK; OSCILLATOR; SOCIAL NETWORK; TELECOMMUNICATION;

EID: 84902438827     PISSN: None     EISSN: 20411723     Source Type: Journal    
DOI: 10.1038/ncomms5079     Document Type: Article

References (41)

1. Motter, A. E., Myers, S. A., Anghel, M. & Nishikawa, T. Spontaneous synchrony in power-grid networks. Nat. Phys. 9, 191-197 (2013).
2. Pecora, L. M. & Carroll, T. L. Master stability functions for synchronized coupled systems. Phys. Rev. Lett. 80, 2109-2112 (1998). (Pubitemid 128621504)
3. Zhou, C. & Kurths, J. Hierarchical synchronization in complex networks with heterogeneous degrees. Chaos 16, 015104 (2006).
4. Do, A.-L., Hofener, J. & Gross, T. Engineering mesoscale structures with distinct dynamical implications. New J. Phys. 14, 115022 (2012).
5. Dahms, T., Lehnert, J. & Schooll, E. Cluster and group synchronization in delay-coupled networks. Phys. Rev. E 86, 016202 (2012).
6. Fu, C., Deng, Z., Huang, L. & Wang, X. Topological control of synchronous patterns in systems of networked chaotic oscillators. Phys. Rev. E 87, 032909 (2013).
7. Kanter, I., Zigzag, M., Englert, A., Geissler, F. & Kinzel, W. Synchronization of unidirectional time delay chaotic networks and the greatest common divisor. Europhys. Lett. 93, 6003 (2011).
8. Rosin, D. P., Rontani, D., Gauthier, D. J. & Scholl, E. Control of synchronization patterns in neural-like boolean networks. Phys. Rev. Lett. 110, 104102 (2013).
9. Sorrentino, F. & Ott, E. Network synchronization of groups. Phys. Rev. E 76, 056114 (2007).
10. Williams, C. R. S. et al. Experimental observations of group synchrony in a system of chaotic optoelectronic oscillators. Phys. Rev. Lett. 110, 064104 (2013).
11. Belykh, V. N., Osipov, G. V., Petrov, V. S., Suykens, J. A. K. & Vandewalle, J. Cluster synchronization in oscillatory networks. Chaos 18, 037106 (2008).
12. D'Huys, O., Vicente, R., Erneux, T., Danckaert, J. & Fischer, I. Synchronization properties of network motifs: Influence of coupling delay and symmetry. Chaos 18, 037116 (2008).
13. Nicosia, V., Valencia, M., Chavez, M., Diaz-Guilera, A. & Latora, V. Remote synchronization reveals network symmetries and functional modules. Phys. Rev. Lett. 110, 174102 (2013).
14. Russo, G. & Slotine, J.-J. E. Symmetries, stability, and control in nonlinear systems and networks. Phys. Rev. E 84, 041929 (2011).
15. Golubitsky, M., Stewart, I. & Schaeffer, D. G. Singularities and Groups in Bifurcation Theory Vol. II (Springer-Verlag, New York, NY, 1985).
16. Golubitsky, M. & Stewart, I. The Symmetry Perspective: From Equilibrium to Chaos in Phase Space and Physical Space (Berkhauser-Verlag, Basel, 2002).
17. Judd, K. Networked dynamical systems with linear coupling: synchronisation patterns, coherence and other behaviours. Chaos 23, 043112 (2013).
18. Fink, K. S., Johnson, G., Carroll, T., Mar, D. & Pecora, L. Three-oscillator systems as universal probes of coupled oscillator stability. Phys. Rev. E 61, 5080-5090 (2000).
19. Irving, D. & Sorrentino, F. Synchronization of dynamical hypernetworks: dimensionality reduction through simultaneous block-diagonalization of matrices. Phys. Rev. E 86, 056102 (2012).
20. Arenas, A., Diaz-Guilera, A. A., Kurths, J., Moreno, Y. & Zhou, C. Synchronization in complex networks. Phys. Rep. 469, 93-153 (2008).
21. Newman, M. Networks, An Introduction Ch. 18 (Oxford University Press, 2011).
22. Tinkham, M. Group Theory and Quantum Mechanics (McGraw-Hill, New York, NY, 1964).
23. Stein, William. SAGE: Software for Algebra an Geometry Experimentation (http://www.sagemath.org/sage/; http://sage.scipy.org/, 2013).
24. The GAP Group. GAP: Groups, Algorithms, and Programming, Version, 4-4 (http://www.gap-system.org, 2005).
25. Vallentin, F. 'Symmetry in semidefinite programs, '. Linear Algebra Appl. 430, 360-369 (2009).
26. Goodman, R. & Wallach, N. R. Representations and Invariants of the Classical Groups (Cambridge University Press, 1998).
27. Hagerstrom, A. M. et al. Experimental observation of chimeras in coupled-map lattices. Nat. Phys. 8, 658-661 (2012).
28. MacArthur, B. D. & Sanchez-Garcia, R. J. Spectral characteristics of network redundancy. Phys. Rev. E 80, 026117 (2009).
29. MacArthur, B. D., Sanchez-Garcia, R. J. & Anderson, J. W. On automorphism groups of networks. Discrete Appl. Math. 156, 3525-3531 (2008).
30. Dionne, B., Golubitsky, M. & Stewart, I. Coupled cells with internal symmetry: I. wreath products. Nonlinearity 9, 559-574 (1996). (Pubitemid 126689416)
31. Bollobas, B. & Riordan, O. M. Handbook of Graphs and Networks (eds Bornholdt, S. & Schuster, H. G.) (Wiley-VCH, Weinheim, 2003).
32. Barabasi, A.-L. & Albert, R. Emergence of scaling in random networks. Science 286, 509-512 (1999).
33. Albert, R. & Barabasi, A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 48-96 (2002).
34. Watts, Duncan J. & Strogatz, Steven H. Collective dynamics of 'smallworld' networks. Nature 393, 440-442 (1998)
35. Nepal electricity authority annual report 2011. available at www.nea.org.np (2011).
36. Abdollahy, S., Lavrova, O., Mammoli, A., Willard, S. & Arellano, B. Innovative Smart Grid Technologies (ISGT), 2012 IEEE PES 1-6 (IEEE, 2012).
37. Abrams, D. M. & Strogatz, S. H. Chimera states for coupled oscillators. Phys. Rev. Lett. 93, 174102 (2004).
38. Laing, C. R. The dynamics of chimera states in heterogeneous Kuramoto networks. Phys. D 238, 1569-1588 (2009).
39. Belykh, V. N., Belykh, I. V. & Hasler, M. Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems. Phys. Rev. E 62, 6332-6345 (2000). (Pubitemid 32033313)
40. Sagan, B. E. The Symmetric Group (Wadsworth Brooks, Pacific Grove, CA, 1991)
41. Hagerstrom, A. Network Symmetries and Synchronization (https://sourceforge.net/projects/networksym/, 2014).