Phase transition in a class of non-linear random networks

TL;DR

This paper investigates the dynamics of non-linear random networks, revealing a phase transition at a critical connectivity point where correlation and complexity are maximized, indicating optimal coordination of behavior.

Contribution

It demonstrates the existence of an order-chaos phase transition in non-linear random networks at a specific connectivity, extending understanding of criticality in complex systems.

Findings

Phase transition at critical connectivity k=2

Maximized correlation and complexity at critical point

Consistent with previous studies on Boolean and threshold networks

Abstract

We discuss the complex dynamics of a non-linear random networks model, as a function of the connectivity k between the elements of the network. We show that this class of networks exhibit an order-chaos phase transition for a critical connectivity k = 2. Also, we show that both, pairwise correlation and complexity measures are maximized in dynamically critical networks. These results are in good agreement with the previously reported studies on random Boolean networks and random threshold networks, and show once again that critical networks provide an optimal coordination of diverse behavior.