Designing Chaotic Attractors: A Semi-supervised Approach

TL;DR

This paper introduces a semi-supervised method using reservoir computing to design chaotic attractors with specific shapes by leveraging bifurcations and untrained dynamics, enabling controlled chaos generation.

Contribution

It presents a novel approach that combines reservoir computing and bifurcation analysis to design chaos with desired geometries using minimal supervision.

Findings

Successfully generates chaos with targeted shapes

Reveals inherent chaos through bifurcation-induced untraining

Provides a framework for semi-supervised chaos design

Abstract

Chaotic dynamics are ubiquitous in nature and useful in engineering, but their geometric design can be challenging. Here, we propose a method using reservoir computing to generate chaos with a desired shape by providing a periodic orbit as a template, called a skeleton. We exploit a bifurcation of the reservoir to intentionally induce unsuccessful training of the skeleton, revealing inherent chaos. The emergence of this untrained attractor, resulting from the interaction between the skeleton and the reservoir's intrinsic dynamics, offers a novel semi-supervised framework for designing chaos.