Self-organizing dynamical networks able to learn autonomously

Abstract

We present a model for the time evolution of network architectures based on dynamical systems. We show that the evolution of the existence of a connection in a network can be described as a stochastic non-Markovian telegraphic signal (NMTS). Such signal is formulated in two ways: as an algorithm and as the result of a system of differential equations. The autonomous learning conjecture (Kaluza P. and Mikhailov A. S., Phys. Rev. E, 90 (2014) 030901(R)) is implemented in the proposed dynamics. As a result, we construct self-organizing dynamical systems (networks) able to modify their structures in order to learn prescribed target functionalities. This theory is applied to two systems: the flow processing networks with time-programmed responses, and a system of first-order chemical reactions. In both cases, we show examples of the evolution and a statistical analysis of the obtained functional networks with respect to the model parameters.