Reconstructing bifurcation diagrams of chaotic circuits with reservoir computing.

Haibo Luo, Yao Du, Huawei Fan, Xuan Wang, Jianzhong Guo, Xingang Wang
Author Information
  1. Haibo Luo: School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China.
  2. Yao Du: School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China.
  3. Huawei Fan: School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China.
  4. Xuan Wang: School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China.
  5. Jianzhong Guo: School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China.
  6. Xingang Wang: School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China.

Abstract

Model-free reconstruction of bifurcation diagrams of Chua's circuits using the technique of parameter-aware reservoir computing is investigated. We demonstrate that (1) reservoir computer can be utilized as a noise filter to restore the system dynamics from noisy signals; (2) for a single Chua circuit, a 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; and (3) for two coupled chaotic Chua circuits with 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. Our 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.

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