On the complexity of the classification of synchronizing graphs

Communications in Computer and Information Science

Volumn 121 CCIS, Issue , 2010, Pages 186-195

  Canale, Eduardo ^a   Monzón, Pablo ^a   Robledo, Franco ^a  

^a Instituto de Matematica y Estadistica Prof Ing Rafael Laguardia   (Uruguay)

Author keywords

coupled oscillators; graph complexity; Network synchronization; synchronizing graphs

Indexed keywords

CONNECTED GRAPH; COUPLED OSCILLATORS; GLOBAL SYNCHRONIZATION; GRAPH COMPLEXITY; INDUCED SUBGRAPHS; INTEGER PARAMETERS; NETWORK SYNCHRONIZATION; NEW RESULTS; SQUARE ROOTS; STRUCTURAL COMPLEXITY; SYNCHRONIZABILITY; SYNCHRONIZING GRAPHS;

COMPUTATIONAL COMPLEXITY; GRAPHIC METHODS; INFORMATION TECHNOLOGY; MESH GENERATION; OSCILLATORS (ELECTRONIC); OSCILLATORS (MECHANICAL); SYNCHRONIZATION;

GRAPH THEORY;

EID: 78650785096     PISSN: 18650929     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-17625-8_19     Document Type: Conference Paper

References (17)

1. Kuramoto, Y.: International Symposium on Mathematical Problems in Theoretical Physics. Lecture Notes in Physics, vol. 39, p. 420 (1975)
2. Winfree, A.: The geometry of biological time. Springer, Heidelberg (1980)
3. Strogatz, S.H.: From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled nonlinear oscillators. Physica D (143), 1-20 (2000)
4. van der Pol, B.: The nonlinear theory of electrical oscillations. Proc. of the Institute of Radio Engineers 22(9), 1051-1086 (1934)
5. Jadbabaie, A., Barahona, M., Motee, N.: On the stability of the Kuramoto model of coupled nonlinear oscillators. In: Proc. of the American Control Conference (2004)
6. Monzón, P., Paganini, F.: Global considerations on the kuramoto model of sinusoidally coupled oscillators. In: Proc. of the 44th IEEE CDC and ECC, Sevilla, Spain, pp. 3923-3928 (2005)
7. Lin, Lin: The mathematical research for the Kuramoto model of the describing neuronal synchrony in the brain. Commun. Nonlinear Sci. Numer. Simulat. 14, 3258-3260 (2009)
8. Chopra, Spong: On exponential synchronization of Kuramoto coupled oscillators. IEEE Transactions on Automatic Control 54(2), 353-357 (2009)
9. Monzón, P.: Almost global stabilityt of dynamical systems. Ph.D. dissertation, Udelar, Uruguay (2006)
10. Canale, E., Monzón, P.: Gluing Kuramoto coupled oscillators networks. In: Proc. of the 46th IEEE Conference on Decision and Control, New Orleans, USA, pp. 4596-4601 (2007)
11. Canale, E., Monzón, P.: Synchronizing graphs, In: Workshop on Spectral Graph Theory with applications on computer science, combinatorial optimization and chemistry (2008)
12. Canale, E., Monzón, P., Robledo, F.: Global Synchronization Properties for Different Classes of Underlying Interconnection Graphs for Kuramoto Coupled Oscillators. In: Lee, Y.-h., Kim, T.-h., Fang, W.-c., Ślȩzak, D. (eds.) FGIT 2009. LNCS, vol. 5899, pp. 104-111. Springer, Heidelberg (2009)
13. Mallada, Tang: Synchronization of Phase-coupled oscillators with arbitrary topology. In: American Control Conference (2010)
14. Biggs, N.: Algebraic Graph theory. Cambridge University Press, Cambridge (1993)
15. Khalil, H.: Nonlinear Systems. Prentice-Hall, Ed. Prentice-Hall, Englewood Cliffs (1996)
16. Canale, E., Monzón, P.: On the characterization of Families of Synchronizing Graphs of Kuramoto Coupled Oscillators. In: IFAC Workshop on Estimation and Control of Networked Systems (NecSys 2009), Venice, Italy (2009)
17. Canale, E., Monzón, P.: Global properties of Kuramoto bidirectionally coupled oscillators in a ring structure. In: IEEE International Conference on Control Applications (CCA) & International Symposium on Intelligent Control (ISIC), Saint Petersburg, Russia, pp. 183-188 (2009)