Order-disorder transition in the Chialvo-Bak `minibrain' controlled by network geometry

TL;DR

This study investigates a biologically-inspired neural network, revealing a geometry-driven phase transition between order and disorder, with scale-free behavior at criticality, independent of noise influences.

Contribution

It demonstrates that network geometry alone can induce a non-equilibrium phase transition in the Chialvo-Bak minibrain model, highlighting the role of interference in network phases.

Findings

Identified a geometry-controlled phase transition.

Observed scale-free behavior at the critical point.

Transition is independent of noise factors.

Abstract

We examine a simple biologically-motivated neural network, the three-layer version of the Chialvo-Bak `minibrain' [Neurosci. 90 (1999) 1137], and present numerical results which indicate that a non-equilibrium phase transition between ordered and disordered phases occurs subject to the tuning of a control parameter. Scale-free behaviour is observed at the critical point. Notably, the transition here is due solely to network geometry and not any noise factor. The phase of the network is thus a design parameter which can be tuned. The phases are determined by differing levels of interference between active paths in the network and the consequent accidental destruction of good paths.