Eur. Phys. J. B (2017) 90: 94
https://doi.org/10.1140/epjb/e2017-70714-7

Regular Article

Autonomous learning by simple dynamical systems with a discrete-time formulation

¹ Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Cuyo, Padre Contreras 1300, 5500 Mendoza, Argentina
² Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), CONICET – Universidad Nacional de Mar del Plata, Funes 3350, 7600 Mar del Plata, Argentina
³ Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Godoy Cruz 2290 (C1425FQB) CABA, Argentina

^a e-mail: pkaluza@mendoza-conicet.gob.ar

Received: 6 December 2016
Received in final form: 13 January 2017
Published online: 17 May 2017

Abstract

We present a discrete-time formulation for the autonomous learning conjecture. The main feature of this formulation is the possibility to apply the autonomous learning scheme to systems in which the errors with respect to target functions are not well-defined for all times. This restriction for the evaluation of functionality is a typical feature in systems that need a finite time interval to process a unit piece of information. We illustrate its application on an artificial neural network with feed-forward architecture for classification and a phase oscillator system with synchronization properties. The main characteristics of the discrete-time formulation are shown by constructing these systems with predefined functions.