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Abstract:

We investigate the behavior of the order parameter describing the collective dynamics of a large set of driven, globally coupled excitable units. We derive conditions on the parameters of the system that allow to bound the degree of synchrony of its solutions. We describe a regime where time dependent nonsynchronous dynamics occurs and, yet, the average activity displays low dimensional, temporally complex behavior. © 2011 American Institute of Physics.

Registro:

Documento: Artículo
Título:Average dynamics of a driven set of globally coupled excitable units
Autor:Alonso, L.M.; Mindlin, G.B.
Filiación:Department of Physics, FCEyN, UBA, Ciudad Universitaria Pab I, cp 1428, Buenos Aires, Argentina
Año:2011
Volumen:21
Número:2
DOI: http://dx.doi.org/10.1063/1.3574030
Título revista:Chaos
Título revista abreviado:Chaos
ISSN:10541500
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10541500_v21_n2_p_Alonso

Referencias:

  • Kuramoto, Y., (1975) Self-Entrainment of a Population of Coupled Nonlinear Oscillators, Lecture Notes in Physics, 39, pp. 420-422. , (Springer, New York)
  • Ott, E., Antonsen, T.M., (2008) Chaos, 18, p. 037113. , 10.1063/1.2930766
  • Ott, E., Antonsen, T.M., (2009) Chaos, 19, p. 023117. , 10.1063/1.3136851
  • Childs, L.M., Strogatz, S.H., (2008) Chaos, 18, p. 043128. , 10.1063/1.3049136
  • Pikovsky, A., Rosenblum, M., Kurths, J., (2001) Synchronization: A Universal Concept in Nonlinear Science, , (Cambridge University Press, Cambridge)
  • Although the results by Ott and Antonsen are strictly valid for N, the average dynamics of a few hundred oscillators was well captured by the order parameters obeying 12; Gilmore, R., Lefranc, M., (2002) The Topology of Chaos, , (Wiley, Hoboken)
  • Hoppensteadt, F.C., Izhikevich, E.M., (1997) Weakly Connected Neural Networks, , and (Springer-Verlag, New York)
  • Alonso, L.M., Alliende, J.A., Mindlin, G.B., (2010) Eur. J. Phys. D, 60, p. 361. , 10.1140/epjd/e2010-00225-2
  • Golubitsky, M.S., Stewart, I., Buono, P.-L., Collins, J.J., (1999) Nature (London), 410, p. 693. , 10.1038/44416
  • Trevisan, M.A., Mindlin, G.B., Goller, F., (2006) Phys. Rev. Lett., 96, p. 058103. , 10.1103/PhysRevLett.96.058103
  • Alonso, L.M., Alliende, J.A., Goller, F., Mindlin, G.B., (2009) Phys. Rev. E, 79, p. 041929. , 10.1103/PhysRevE.79.041929
  • Lorenz, E.N., (1963) J. Atmos. Sci., 20, p. 130. , 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2

Citas:

---------- APA ----------
Alonso, L.M. & Mindlin, G.B. (2011) . Average dynamics of a driven set of globally coupled excitable units. Chaos, 21(2).
http://dx.doi.org/10.1063/1.3574030
---------- CHICAGO ----------
Alonso, L.M., Mindlin, G.B. "Average dynamics of a driven set of globally coupled excitable units" . Chaos 21, no. 2 (2011).
http://dx.doi.org/10.1063/1.3574030
---------- MLA ----------
Alonso, L.M., Mindlin, G.B. "Average dynamics of a driven set of globally coupled excitable units" . Chaos, vol. 21, no. 2, 2011.
http://dx.doi.org/10.1063/1.3574030
---------- VANCOUVER ----------
Alonso, L.M., Mindlin, G.B. Average dynamics of a driven set of globally coupled excitable units. Chaos. 2011;21(2).
http://dx.doi.org/10.1063/1.3574030