用一台机器同时推断两个混沌系统的分岔图，仅需少量观测数据。
Inferring bifurcation diagrams of two distinct chaotic systems by a single machine
- 通过双通道重构器，融合系统标签与参数控制信号。
- 不仅能预测短期演化，还能复现长期统计特性并重建分岔图。
- 适合研究多系统共存的复杂动力学，如实验电路与数值模拟。
我们提出一种双通道储备池计算方案，仅用一台机器即可推断两个不同混沌系统的动态行为。通过在标准储备池中引入系统标签通道和参数控制通道，该机器可基于从两个系统少数采样状态收集的时间序列进行训练。结果表明，训练后的机器不仅能预测采样状态的短期演化，还能重现未见状态的长期统计特性，从而实现从部分观测中重建两个系统的分岔图。该方法在数值仿真中应用于洛伦兹与罗素系统，在实验中应用于蔡氏电路与罗斯勒电路中均验证了有效性。功能网络分析进一步显示，两个目标系统在储备池中以不同的动力学模式被编码。这些结果拓展了多功能与参数感知的储备池计算，为利用单台机器实现多非线性系统的数据驱动推断提供了新路径。
原文摘要 · Abstract (English)
We propose a dual-channel reservoir-computing scheme for inferring the dynamics of two distinct chaotic systems with a single machine. By augmenting a standard reservoir with a system-label channel and a parameter-control channel, the machine can be trained from time series collected from a few sampled states of the two systems. We show that the trained machine not only predicts the short-time evolution of the sampled states, but also reproduces the long-term statistical properties of unseen states, thereby enabling reconstruction of the bifurcation diagrams of both systems from partial observations. The effectiveness of the scheme is demonstrated for the Lorenz and Rössler systems in numerical simulations and for the Chua and Rossler circuits in experiments. Functional-network analysis further shows that the two target systems are encoded by distinct dynamical patterns in the reservoir. These results extend multifunctional and parameter-aware reservoir computing, and provide a route to data-driven inference of multiple nonlinear systems using a single machine.
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