In recent years, the generation of rigorously provable chaos in finite precision digital domain has made a lot of progress in theory and practice, this article is a part of it. It aims to improve and expand the theoretical and application framework of higher-dimensional digital chaotic system (HDDCS). In this study, topological mixing for HDDCS is strictly proved theoretically at first. Topological mixing implies Devaney's definition of chaos in compact space, but not vise versa. Therefore, the proof of topological mixing improves and expands the theoretical framework of HDDCS. Then, a general design method for constructing HDDCS via loop-state contraction algorithm is given. The construction of the iterative function uncontrolled by random sequences (hereafter called iterative function) is the starting point of this research. On this basis, this article put forward a general design method to solve the problem of HDDCS construction, and a number of examples illustrate the effectiveness and feasibility of this method. The adjacency matrix corresponding to the designed HDDCS is used to construct the chaotic echo state network (ESN) for the Mackey-Glass time series prediction. The prediction accuracy is improved with the increase of the size of the reservoir and the dimension of HDDCS, indicating that higher-dimensional systems have better prediction performance than lower-dimensional systems.
Constructing low-dimensional ordinary differential equations from chaotic time series of high/infinite-dimensional systems using radial function-based regression
Data-driven characterization of spatiotemporal chaos using ensemble reservoir computing
School of Physical Science and Technology, Beijing University of Posts and Telecommunications（北京邮电大学物理科学与技术学院）；State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications（北京邮电大学信息光子学与光通信国家重点实验室）
Unfolded Krylov complexity: universal chaotic dynamics without false positives
Julius-Maximilians-Universität Würzburg（维尔茨堡大学）；Shanghai Jiao Tong University（上海交通大学）；Pohang University of Science and Technology（韩国科学技术院）；Instituto de Física Teórica UAM/CSIC（马德里自治大学/西班牙国家科学研究委员会理论物理研究所）
