Life is not on the edge of chaos but in a half-chaos of not fully random systems. Definition and simulations of the half-chaos in complex networks

TL;DR

This paper introduces the concept of half-chaos in complex networks, showing that many real-world systems operate in this intermediate state rather than at the edge of chaos, which broadens understanding of system stability and evolution.

Contribution

It defines and demonstrates the existence of half-chaotic networks through simulations, challenging the traditional view that systems are either ordered or chaotic, and provides a new framework for modeling complex adaptive systems.

Findings

Half-chaos exists as a third state between order and chaos.

Many real-world systems exhibit features of half-chaos, not full chaos.

Half-chaos allows for more stable yet adaptable system modeling.

Abstract

The research concerns the dynamics of complex autonomous Kauffman networks. The article defines and shows using simulation experiments half-chaotic networks, which exhibit features much more similar to typically modeled systems like a living, technological or social than fully random Kauffman networks. This makes a large change of widely taken view in the dynamics of complex networks. Current theory predicts that random autonomous systems can be either ordered or chaotic with fast phase transition between them. However, modeled adapted systems are not fully random, they are usually stable, but the estimated parameters are usually "chaotic", they place the fully random networks in the chaotic regime, far from the narrow phase transition. It is showed that among the not fully random systems with "chaotic parameters", a large third state called half-chaos exists, which simultaneously exhibit small (ordered) and large (chaotic) reactions for small disturbances in similar share. The discovery of half-chaos frees modeling of adapted systems from sharp restrictions; it allows to use "chaotic parameters" and get a nearly stable system more similar to modeled one. It gives a base for identity criterion of an evolving object, simplifies the definition of basic Darwinian mechanism and changes "life on the edge of chaos" to "life evolves in the half-chaos of not fully random systems".