On the Origin of Chaos in Autonomous Boolean Networks

TL;DR

This paper investigates the origins of chaos in autonomous Boolean networks, identifying specific non-ideal features of logic gates that can induce chaotic behavior, with implications for technological applications and fundamental studies.

Contribution

It systematically analyzes how non-ideal gate features like degradation lead to chaos, advancing understanding of chaotic dynamics in real-world Boolean networks.

Findings

Degradation can generate chaos in Boolean networks.

Short-pulse rejection and asymmetry promote periodic behavior.

Deterministic chaos is likely in many experimental Boolean-like networks.

Abstract

We undertake a systematic study of the dynamics of Boolean networks to determine the origin of chaos observed in recent experiments. Networks with nodes consisting of ideal logic gates are known to display either steady states, periodic behavior, or an ultraviolet catastrophe where the number of logic-transition events circulating in the network per unit time grows as a power-law. In an experiment, non-ideal behavior of the logic gates prevents the ultraviolet catastrophe and may lead to deterministic chaos. We identify certain non-ideal features of real logic gates that enable chaos in experimental networks. We find that short-pulse rejection and the asymmetry between the logic states tends to engender periodic behavior, at least for the simplest networks. On the other hand, we find that a memory effect termed "degradation" can generate chaos. Our results strongly suggest that deterministic chaos can be expected in a large class of experimental Boolean-like networks. Such devices may find application in a variety of technologies requiring fast complex waveforms or flat power spectra, and can be used as a test-bed for fundamental studies of real-world Boolean-like networks.