Interdisciplinary Nonlinear Dynamics 438-3:

Networks of Coupled Active Elements

Hermann Riecke & Sara Solla

Spring Quarter 2002


  1. Globally coupled oscillators - Kuramoto model [1,2,3]
  2. Integrate-and-Fire Models of Neurons [4]
  3. Complex Ginzburg-Landau equation [5,6,7]
  4. Dynamics of small-world networks [8,9,10]


S. H. Strogatz. From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators. Physica D, 143(1-4):1-20, September 2000.

Y. Kuramoto. Chemical oscillations, waves, and turbulence, volume 19 of Springer series in synergetics. Springer, 1984.

K. Wiesenfeld, P. Colet, and S. H. Strogatz. Synchronization transitions in a disordered Josephson series array. Phys. Rev. Lett., 76(3):404-407, January 1996.

P. C. Bressloff and S. Coombes. Dynamics of strongly coupled spiking neurons. Neural Comput., 12(1):91, January 2000.

I. S. Aranson and L. Kramer. The world of the complex Ginzburg-Landau equation. Rev. Mod. Phys., 74:99, 2002.

M. van Hecke. The building blocks of spatiotemporal intermittency. Phys. Rev. Lett., 80:1896, 1998.

L. Brusch, A. Torcini, M. van Hecke, G. Zimmermann, and M. Baer, Modulated amplitude waves and defect formation in the one-dimensional complex Ginzburg-Landau equation. Physica D, 160:127, 2001.

L. F. Lago-Fernandez, R. Huerta, F. Corbacho, and J. A. Siguenza. Fast response and temporal coherent oscillations in small-world networks. Phys. Rev. Lett., 84(12):2758-2761, March 2000.

H. Hong, M. Y. Choi, and B. J. Kim. Synchronization on small-world networks. Phys. Rev. E, 65(2):026139, February 2002.

X. F. Wang and G. R. Chen. Synchronization in small-world dynamical networks. Int. J. Bifurcation Chaos, 12(1):187-192, January 2002.

The other papers can be easily retrieved from the APS web journal site.