Complexity Matching and Requisite Variety

TL;DR

This paper explores how matching the complexity of crucial events, characterized by inverse power law distributions, facilitates synchronization and information transfer between complex systems, with implications for biofeedback therapies.

Contribution

It introduces a novel complexity matching mechanism based on the shared IPL index that enhances synchronization beyond chaos synchronization.

Findings

Complex systems with the same IPL index μ synchronize perfectly.

Crucial events influence information transport and system synchronization.

Complexity matching improves biofeedback therapy effectiveness.

Abstract

Complexity matching characterizes the role of information in interactions between systems and can be traced back to the 1957 Introduction to Cybernetics by Ross Ashby. We argue that complexity can be expressed in terms of crucial events, which are generated by the processes of spontaneous self-organization. Complex processes, ranging from biological to sociological, must satisfy the homeodynamic condition and host crucial events that have recently been shown to drive the information transport between complex systems. We adopt a phenomenological approach, based on the subordination to periodicity that makes it possible to combine homeodynamics and self-organization induced crucial events. The complexity of crucial events is defined by the waiting-time probability density function (PDF) of the intervals between consecutive crucial events, which have an inverse power law (IPL) PDF $\psi (\tau )\propto 1/(\tau )^{\mu }$ with $1<\mu <3$. We show that the action of crucial events has an effect compatible with the shared notion of complexity-induced entropy reduction, while making the synchronization between systems sharing the same complexity different from chaos synchronization. We establish the coupling between two temporally complex systems using a phenomenological approach inspired by models of swarm cognition and prove that complexity matching, namely sharing the same IPL index $\mu $, facilitates the transport of information, generating perfect synchronization. This new form of complexity matching is expected to contribute significantly to progress in understanding and improving biofeedback therapies.