Autonomous dynamical systems based on hardware implementations of delay-reservoir computers

Reservoir computing (RC) is a machine learning technique allowing for novel approaches to realize trainable autonomous nonlinear oscillators. Here we employ delay-based echo state networks with output feedback, simple yet powerful implementations of neuromorphic systems, to reproduce the dynamical behavior of a Rössler chaotic system. Our hardware implementation relies on a delay-based RC topology, and consists of two main elements: an analog Mackey Glass nonlinearity and a Raspberry Pi board. We demonstrate the capacity of our experiment to generate chaotic time-traces in an autonomous manner, and we prove that noise can play a constructive role in the training process, when realizing nonlinear oscillators based on closed-loop operation. We use phase-space reconstruction of the chaotic attractor and the comparison of the frequency spectra, along with recurrence quantification analysis (RQA), to perform a nonlinear data analysis with the aim of comparing the autonomous operation and the original time-series in more detail.