Regensburg 2007 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 30: Poster II
DY 30.19: Poster
Thursday, March 29, 2007, 16:00–18:00, Poster D
Topological self-organization and critical dynamics of input-driven threshold networks — •Thimo Rohlf — Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
Based on a simple model of network self-organization by local rewiring rules [1], we study topological evolution of input-driven neural threshold networks. In addition to the original system, a subset of network nodes is driven by external input signals with a spiking rate ρin, that serves as a convenient new control parameter. Depending on ρin > 0, we find a much faster convergence towards topological and dynamical criticality [2] than in the original model (which has ρin = 0).
In particular, our extensive numerical simulations indicate that, at a critical driving rate ρinc(N), networks become self-organized critical even for finite numbers N of nodes. Several dynamical order parameters exhibit pronounced power-law scaling, long-range correlations and 1/f noise (including, e.g., the distribution of asymptotic Hamming distances of initially nearby system states).
Finally, we discuss possible applications of this model to problems in two fields: control of neural activity in the brain, and the evolution of signal processing by gene regulatory networks in biological cells.
[1] S. Bornholdt and T. Rohlf, Phys. Rev. Lett. 84, 6114 (2000)
[2] T. Rohlf and S. Bornholdt, Physica A 310, 245-259 (2002)