利用储层计算重构混沌电路的分岔图
Reconstructing bifurcation diagrams of chaotic circuits with reservoir computing
AI总结：
本文提出利用参数感知储层计算从含噪时间序列中重构蔡氏电路分岔图，并预测耦合混沌电路的同步程度变化，验证了该技术在真实混沌系统分岔图重构中的应用潜力。
摘要：
本文研究了利用参数感知储层计算技术对蔡氏电路的分岔图进行无模型重构。我们证明了：(1) 储层计算机可用作噪声滤波器，从含噪信号中恢复系统轨迹；(2) 对于单个蔡氏电路，使用在若干采样状态处测得的含噪时间序列训练的机器能够高精度地重构该电路的整个分岔图；(3) 对于两个参数不匹配的耦合混沌蔡氏电路，使用在若干耦合强度处测得的含噪时间序列训练的机器能够在较大范围内预测耦合电路同步程度随耦合强度的变化。这些研究验证了参数感知储层计算技术从含噪信号中学习混沌电路动力学的能力，表明该技术在重构现实世界混沌系统分岔图方面具有潜在应用价值。
英文摘要：
Model-free reconstruction of the bifurcation diagrams of Chua's circuits by the technique of parameter-aware reservoir computing is investigated. We demonstrate that: (1) reservoir computer can be utilized as a noise filter to recover the system trajectory from noisy signals; (2) for a single Chua circuit, the 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; (3) for two coupled chaotic Chua circuits of 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. The 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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