Instability, complexity, and evolution
type: Item
instance of: scholarly article
title: Instability, complexity, and evolution
zbMATH Open document ID: 1211.37121
author: J. Blot
published in: Journal of Mathematical Sciences (New York)
publication date: 2009-11-13T00:00:00Z
review text: Consider random dynamical systems generated by neural networks and complex circuits. The authors discuss the viability problem, i.e. conditions under which the system state is in a prescribed domain of the phase space with probability one or with high probability as time \(t\) tends to infinity (a property called stability). They show that stabilizing evolutions of unstable systems possess a related Kolmogorov complexity which cannot be bounded by a constant as \(t \to \infty\). Examples of stable evolution are given. Here, evolution is understood as a Markov process of modification of the discrete code of system parameters.
reviewed by: Henri Schurz
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 68Q30
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 93E15
zbMATH DE Number: 5632966
zbMATH Keywords: random dynamical systems
zbMATH Keywords: neural networks
zbMATH Keywords: biological circuits
zbMATH Keywords: complex structures
zbMATH Keywords: reaction-diffusion equations
zbMATH Keywords: structural stability
zbMATH Keywords: genericity
zbMATH Keywords: viability
zbMATH Keywords: ergodic theory
zbMATH Keywords: Pfaffian functions
zbMATH Keywords: Noetherian functions
zbMATH Keywords: Kolmogorov complexity theory
zbMATH Keywords: stochastic stability
MaRDI profile type: Publication
full work available at URL: s10958-009-9412-4
OpenAlex ID: W2088805247
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DOI: 10.1007/S10958-009-9412-4
description: scientific article; zbMATH DE number 5632966