Functional optimization in complex excitable networksS. Johnson, J. Marro and J. J. Torres
Departamento de Electromagnetismo y Física de la Materia, and Institute "Carlos I" for Theoretical and Computational Physics, Facultad de Ciencias, Universidad de Granada - 18071-Granada, Spain, EU
received 10 April 2008; accepted in final form 1 July 2008; published August 2008
published online 19 August 2008
We study the effect of varying wiring in excitable random networks in which connection weights change with activity to mold local resistance or facilitation due to fatigue. Dynamic attractors, corresponding to patterns of activity, are then easily destabilized according to three main modes, including one in which the activity shows chaotic hopping among the patterns. We describe phase transitions to this regime, and show a monotonous dependence of critical parameters on the heterogeneity of the wiring distribution. Such correlation between topology and functionality implies, in particular, that tasks which require unstable behavior -such as pattern recognition, family discrimination and categorization- can be most efficiently performed on highly heterogeneous networks. It also follows a possible explanation for the abundance in nature of scale-free network topologies.
64.60.an - Finite-size systems.
05.45.-a - Nonlinear dynamics and chaos.
84.35.+i - Neural networks.
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