Functional Optimization in Complex Excitable Networks

TL;DR

This paper investigates how the wiring heterogeneity in excitable networks influences their dynamic behavior, revealing phase transitions and the potential advantages of scale-free topologies for tasks requiring unstable activity patterns.

Contribution

It introduces a detailed analysis of how wiring heterogeneity affects stability and chaos in excitable networks, linking topology to functional capabilities.

Findings

Heterogeneous wiring leads to phase transitions to chaotic regimes.

Critical parameters depend monotonically on wiring heterogeneity.

Scale-free networks are advantageous for unstable, pattern-based tasks.

Abstract

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.