Stability of Boolean and continuous dynamics

TL;DR

This paper compares the stability of Boolean and continuous biological dynamics, revealing that Boolean instability does not necessarily imply instability in the original continuous systems, especially in networks with high sensitivity.

Contribution

It demonstrates that Boolean stability classifications can be misleading, showing that continuous dynamics can remain stable despite Boolean instability, especially in high-sensitivity networks.

Findings

Boolean instability does not imply continuous instability

High sensitivity networks can be stable under small perturbations

Boolean and continuous stability properties differ significantly

Abstract

Regulatory dynamics in biology is often described by continuous rate equations for continuously varying chemical concentrations. Binary discretization of state space and time leads to Boolean dynamics. In the latter, the dynamics has been called unstable if flip perturbations lead to damage spreading. Here we find that this stability classification strongly differs from the stability properties of the original continuous dynamics under small perturbations of the state vector. In particular, random networks of nodes with large sensitivity yield stable dynamics under small perturbations.