Designing Chaotic Attractors: A Semi-supervised Approach
This work addresses the challenge of designing chaotic dynamics for engineering applications, offering a semi-supervised approach that is incremental in its method.
The authors tackled the problem of designing chaotic attractors with desired shapes by proposing a semi-supervised method using reservoir computing, where they induced chaos by exploiting a bifurcation during unsuccessful training of a periodic skeleton, resulting in a novel framework for geometric control of chaos.
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.