基于储备池计算的混沌系统同步行为预测研究

Research on Predicting Synchronization Behavior of Chaotic Systems Based on Reservoir Computing

摘要: 本文基于储备池计算这一机器学习框架，实现了对光滑Chen混沌系统与分段线性Chua混沌系统的无模型同步行为预测。我们首先通过数值模拟生成了两类系统的混沌数据，并训练了回声状态网络以捕捉其动力学特性。随后，系统地研究了单端驱动同步、级联同步以及在参数不匹配条件下的广义同步。研究发现，训练良好的储备池计算机能够通过传递单一标量信号与未知的混沌系统实现同步，并且这种同步现象在级联网络中可以传播。通过对比两类系统的同步误差与收敛速度，我们证实了光滑非线性系统相较于分段线性系统，其同步收敛速度更快、级联误差累积更小，而后者在非线性切换点处表现出更强的误差敏感性和波动性。本研究为理解和预测复杂非线性系统的同步行为提供了新的视角和方法。

Abstract: This paper employs reservoir computing, a machine learning framework, to achieve model-free prediction of synchronization behavior in the smooth Chen chaotic system and the piecewise-linear Chua chaotic system. First, chaotic data for both systems are generated through numerical simulation, and echo state networks are trained to capture their dynamic characteristics. Subsequently, three types of synchronization—unidirectional drive synchronization, cascade synchronization, and generalized synchronization under parameter mismatch—are systematically investigated. The results demonstrate that a well-trained reservoir computer can synchronize with an unknown chaotic system by transmitting only a single scalar signal, and this synchronization can propagate through a cascade network. By comparing the synchronization errors and convergence speeds of the two systems, we find that the smooth nonlinear system exhibits faster synchronization convergence and smaller cascade error accumulation than the piecewise-linear system, while the latter shows stronger error sensitivity and fluctuations at nonlinear switching points. This study provides new insights and methods for understanding and predicting synchronization behavior in complex nonlinear systems.