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

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 represents a large change in the widely held view taken of the dynamics of complex systems. Current theory predicts that random autonomous systems can be either ordered or chaotic with fast phase transition between them. The theory uses shift of finite, discrete networks to infinite and continuous space. This move loses important features like e.g. attractor length, making description too simplified. 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. I show that among the not fully random systems with “chaotic parameters”, a large third state called half-chaos exists. Half-chaotic system simultaneously exhibits 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”.