Temporal, structural, and functional heterogeneities extend criticality and antifragility in random Boolean networks

TL;DR

This paper demonstrates that heterogeneity in time, structure, and function in random Boolean networks broadens the regions of criticality and antifragility, challenging the notion that homogeneity is optimal for these properties.

Contribution

It introduces the idea that heterogeneity extends criticality and antifragility in random Boolean networks, providing a new perspective on the balance between homogeneity and heterogeneity in complex systems.

Findings

Heterogeneity broadens the criticality region in parameter space.

Heterogeneity increases the parameter regions where antifragility is observed.

Maximum antifragility occurs in homogeneous networks at specific parameters.

Abstract

Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger, stronger, or faster than others. In homogeneous systems, criticality -- a balance between change and stability, order and chaos -- is usually found for a very narrow region in the parameter space, close to a phase transition. Using random Boolean networks -- a general model of discrete dynamical systems -- we show that heterogeneity -- in time, structure, and function -- can broaden additively the parameter region where criticality is found. Moreover, parameter regions where antifragility is found are also increased with heterogeneity. However, maximum antifragility is found for particular parameters in homogeneous networks. Our work suggests that the "optimal" balance between homogeneity and heterogeneity is non-trivial, context-dependent, and in some cases, dynamic.