Instability, complexity, and evolution
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.
scientific article; zbMATH DE number 5632966
scientific article