IJCsatellite IJCsatellite/cond-mat

cond-mat/0410171 http://arxiv.org/abs/cond-mat/0410171

Diversity-induced synchronized oscillations in close-to-threshold excitable elements arranged on regular networks: effects of network topology

Authors: I. Vragovi\'c (1), E. Louis (1), C. D. E. Boschi (2), G. J. Ortega (3)

((1) Departamento de Fisica Aplicada, Instituto Universitario de Materiales and Unidada Asociada CSIC-UA, Universidad de Alicante, Spain. (2) INFM Research Unit of Bologna, Bologna, Italia. (3) Departamento de Física, F.C.E.N. Universidad de Buenos Aires and CONICET, Argentine.)

Comments: 11 pages and 13 figures
Subj-class: Disordered Systems and Neural Networks; Biological Physics; Cell Behavior

The question of how network topology influences emergent synchronized oscillations in excitable media is addressed. Coupled van der Pol-FitzHugh-Nagumo elements arranged either on regular rings or on clusters of the square lattice are investigated. Clustered and declustered rings are constructed to have the same number of next-nearest-neighbors (four) and a number of links twice that of nodes. The systems are chosen to be close-to-threshold, allowing global oscillations to be triggered by a weak diversity among the constituents that, by themselves, would be non-oscillating. The results clearly illustrate the crucial role played by network topology. In particular we found that network performance (oscillatory behavior and synchronization) is mainly determined by the network average path length and by the standard deviation of path lengths. The shorter the average path length and the smaller the standard deviation, the better the network performance. Local properties, as characterized by the clustering coefficient, are less important. In addition we comment on the mechanisms that sustain synchronized oscillations and on the transient times needed to reach these stationary regimes.

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