Designing Chaotic Attractors: A Semi-supervised Approach

International Research Center for Neurointelligence, University of Tokyo Institutes for Advanced Study, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan (Dated: July 16, 2024) 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. Chaotic dynamics are prevalent in nature, including biological neural systems [1-3], and are applied in engineering, such as for random number generation [4, 5], communication systems [6, 7], optimization [8, 9], deep learning [10, 11], and robot control [12-14]. A notable challenge is designing the geometric shapes of chaotic attractors, for which no practical methods have been proposed so far, to the best of our knowledge.