Reconstructing bifurcation diagrams of chaotic circuits with reservoir computing

TL;DR

This paper demonstrates that parameter-aware reservoir computing can accurately reconstruct bifurcation diagrams of chaotic circuits from noisy data, enabling analysis of complex dynamics and synchronization in coupled systems.

Contribution

It introduces a novel application of reservoir computing for noise filtering and bifurcation diagram reconstruction in chaotic circuits, including coupled systems.

Findings

Reservoir computing effectively filters noise from chaotic signals.

High-precision reconstruction of bifurcation diagrams from noisy data.

Prediction of synchronization behavior in coupled chaotic circuits.

Abstract

Model-free reconstruction of the bifurcation diagrams of Chua's circuits by the technique of parameter-aware reservoir computing is investigated. We demonstrate that: (1) reservoir computer can be utilized as a noise filter to recover the system trajectory from noisy signals; (2) for a single Chua circuit, the machine trained by the noisy time series measured at several sampling states is capable of reconstructing the whole bifurcation diagram of the circuit with a high precision; (3) for two coupled chaotic Chua circuits of mismatched parameters, the machine trained by the noisy time series measured at several coupling strengths is able to anticipate the variation of the synchronization degree of the coupled circuits with respect to the coupling strength over a wide range. The studies verify the capability of the technique of parameter-aware reservoir computing in learning the dynamics of chaotic circuits from noisy signals, signifying the potential application of this technique in reconstructing the bifurcation diagram of real-world chaotic systems.