### Extreme fluctuations in small-world-coupled autonomous systems with relaxational dynamics

**Guclu, H **

Wednesday 28 June 2006, 14:10-14:20

Seminar Room 1, Newton Institute

#### Abstract

Synchronization is a fundamental problem in natural and artificial coupled multi-component systems. We investigate to what extent small-world couplings (extending the original local relaxational dynamics through the random links) lead to the suppression of extreme fluctuations in the synchronization landscape of such systems. In the absence of the random links, the steady-state landscape is "rough" (strongly de-synchronized state) and the average and the extreme height fluctuations diverge in the same power-law fashion with the system size (number of nodes). With small-world links present, the average size of the fluctuations becomes finite (synchronized state). For exponential-like noise the extreme heights diverge only logarithmically with the number of nodes, while for power-law noise they diverge in a power-law fashion. The statistics of the extreme heights are governed by the Fisher–Tippett–Gumbel and the Fréchet distribution, respectively. We also study the extreme-value scaling and distributions in scale-free networks. We illustrate our findings through an actual synchronization problem in parallel discrete-event simulations.
* http://cnls.lanl.gov/External/people/Hasan_Guclu.php - Homepage
* http://www.rpi.edu/~korniss - Homepage
* http://cnls.lanl.gov/~guclu - Homepage
* http://arxiv.org/abs/cond-mat/0311575 - Preprint

#### Presentation