论文标题
压缩相空间检测非线性动力学系统中的状态变化
Compressing phase space detects state changes in nonlinear dynamical systems
论文作者
论文摘要
控制复杂系统的非线性动力学的方程通常是未知的，间接方法用于重建其歧管。反过来，它们取决于嵌入需要其他方法的参数和长时间的时间序列。在本文中，我们表明，可以通过无损压缩系统的时间过程来实现最佳的重建，从而对其动力学进行自洽分析以及对其复杂性的度量，即使对于短序列也是如此。我们对复杂性的度量检测系统的状态变化，例如弱同步现象，表征许多系统，一步一步，整合了Lyapunov和分形分析的结果。
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences to be accurate. In this paper, we show that an optimal reconstruction can be achieved by lossless compression of system's time course, providing a self-consistent analysis of its dynamics and a measure of its complexity, even for short sequences. Our measure of complexity detects system's state changes such as weak synchronization phenomena, characterizing many systems, in one step, integrating results from Lyapunov and fractal analysis.
