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Center for Nonlinear Studies |
Based on a simple model of network self-organization by local rewiring rules \cite{BornholdtRohlf2000}, we study topological evolution of input-driven neural threshold networks. In addition to the original system analyzed in \cite{BornholdtRohlf2000}, a subset of network nodes is driven by external input signals with a spiking rate $\rho_{in}$, that serves as a convenient new control parameter. Depending on $\rho_{in} > 0$, we find a much faster convergence towards topological and dynamical criticality \cite{RohlfBornholdt2002} than in the original model (which has $\rho_{in} = 0$). In particular, our extensive numerical simulations indicate that, at a critical driving rate $\rho_{in}^c(N)$, 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.