A mathematical model for the dynamics of clustering

Physica D: Nonlinear Phenomena

Volumn 237, Issue 19, 2008, Pages 2517-2530

  Aeyels, Dirk ^a   De Smet, Filip ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

Clustering; Kuramoto model; Multi agent systems; Self organization

Indexed keywords

PHYSICS;

CLUSTER STRUCTURE; CLUSTERING; DIVERSE FIELDS; KURAMOTO MODELS; LONG TERM BEHAVIOURS; NON-IDENTICAL; NUMBER OF CLUSTERS; SELF ORGANIZATIONS;

MULTI AGENT SYSTEMS;

EID: 49749143360     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2008.02.024     Document Type: Article

References (31)

1. D. Aeyels, F. De Smet, A model for the dynamical process of cluster formation, in: 7th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2007, August 2007, pp. 260-264
2. Aeyels D., and Rogge J.A. Existence of partial entrainment and stability of phase locking behavior of coupled oscillators. Progr. Theoret. Phys. 112 6 (2004) 921-942
3. Bordogna C.M., and Albano E.V. Statistical methods applied to the study of opinion formation models: A brief overview and results of a numerical study of a model based on the social impact theory. J. Phys.: Condens. Matter 19 6 (2007) 065144 (16pp)
4. Czirók A., Ben-Jacob E., Cohen I., and Vicsek T. Formation of complex bacterial colonies via self-generated vortices. Phys. Rev. E 54 2 (1996) 1791-1801
5. Daido H. Multibranch entrainment and scaling in large populations of coupled oscillators. Phys. Rev. Lett. 77 7 (1996) 1406-1409
6. De Smet F., and Aeyels D. Partial entrainment in the finite Kuramoto-Sakaguchi model. Physica D 234 2 (2007) 81-89
7. F. De Smet, D. Aeyels, Clustering in a network of non-identical and attractive agents, 2008 (in preparation)
8. F. De Smet, D. Aeyels, Resonance effects and entrainment break up in Kuramoto models with multi-modal frequency densities, Phys. Rev. E (2008) (submitted for publication)
9. Deffuant G., Amblard F., Weisbuch G., and Faure T. How can extremism prevail? A study based on the relative agreement interaction model. J. Artif. Soc. Social Simul. 5 4 (2002)
10. Golomb D., Hansel D., Shraiman B., and Sompolinsky H. Clustering in globally coupled phase oscillators. Phys. Rev. A 45 6 (1992) 3516-3530
11. Grégoire G., Chaté H., and Tu Y. Moving and staying together without a leader. Physica D 181 3-4 (2003) 157-170
12. Hegselmann R., and Krause U. Opinion dynamics and bounded confidence: Models, analysis and simulation. J. Artif. Soc. Social Simul. 5 3 (2002)
13. Jain A.K., Murty M.N., and Flynn P.J. Data clustering: A review. ACM Comput. Surv. 31 3 (1999) 264-323
14. Kuramoto Y. Cooperative dynamics of oscillator community. Progr. Theoret. Phys. 79 suppl. (1984) 223-240
15. Liao T.W. Clustering of time series data-a survey. Pattern Recog. 38 11 (2005) 1857-1874
16. Lohmiller W., and Slotine J. On contraction analysis for non-linear systems. Automatica 34 6 (1998) 683-696
17. Maistrenko Y., Popovych O., Burylko O., and Tass P.A. Mechanism of desynchronization in the finite-dimensional Kuramoto model. Phys. Rev. Lett. 93 8 (2004) 084102
18. Manrubia S.C., Mikhailov A.S., and Zanette D.H. Emergence of Dynamical Order: Synchronization Phenomena in Complex Systems. World Scientific Lecture Notes in Complex Systems vol. 2 (2004), World Scientific
19. Mikhailov A.S., and Zanette D.H. Noise-induced breakdown of coherent collective motion in swarms. Phys. Rev. E 60 4 (1999) 4571+
20. Morelli L.G., Cerdeira H.A., and Zanette D.H. Frequency clustering of coupled phase oscillators on small-world networks. European Phys. J. B 43 (2005) 243-250
21. Okuda K. Variety and generality of clustering in globally coupled oscillators. Physica D 63 3-4 (1993) 424-436
22. Pavlov A., Pogromsky A., van de Wouw N., and Nijmeijer H. Convergent dynamics, a tribute to Boris Pavlovich Demidovich. Systems Control Lett. 52 (2004) 257-261
23. Plapp J.E. Engineering Fluid Mechanics. Series in Engineering of the Physical Sciences (1968), Prentice Hall
24. Reynolds C.W. Flocks, herds, and schools: A distributed behavioral model. SIGGRAPH '87 Conference Proceedings. Comput. Graph. 21 4 (1987) 25-34
25. Strogatz S.H. From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators. Physica D 143 (2000) 1-20
26. Strogatz S.H. SYNC: The Emerging Science of Spontaneous Order (2003), Hyperion Press
27. Sznajd-Weron K., and Sznajd J. Opinion evolution in closed community. Internat. J. Modern Phys. C 11 6 (2000) 1157-1165
28. Tass P. Phase and frequency shifts in a population of phase oscillators. Phys. Rev. E 56 2 (1997) 2043-2060
29. F. Wu, B.A. Huberman, Social structure and opinion formation, Computational Economics 0407002, EconWPA, July 2004. Available at: http://ideas.repec.org/p/wpa/wuwpco/0407002.html
30. Zanette D.H., and Mikhailov A.S. Dynamical clustering in oscillator ensembles with time-dependent interactions. Europhys. Lett. 65 4 (2004) 465-471
31. Zhao Y., and Karypis G. Data clustering in life sciences. Molecular Biotechnol. 31 1 (2005) 55-80