【摘要】 提出一种新的基于辛几何谱的时间序列确定性检测方法,通过计算原始时间序列及其替代数据的辛几何谱,利用非参数Mann-Whitney秩和检验方法,可有效地辨别确定性混沌过程和随机过程.通过对常见的随机过程,Lorenz,Rssler,Mackey-Glass,高维耦合方程的仿真检验,说明了方法的有效性.并通过用SantaFe测试集中两个序列检验了其对实际时间序列的适用性,最后研究不同数据长度和不同强度噪声对该方法性能的影响说明了其鲁棒性.更多还原

【Abstract】 Compared with singular value decomposition,symplectic geometry spectrum is a measure preserving and nonlinear transform.So,it is more suitable for nonlinear dynamics system analysis.A new method to detect determinism in time series based on symplectic geometry spectrum(SGS)is proposed in the present work.Chaos and stochastic process could be recognized by applying the non-parameter Mann-Whitney on the SGS of original data and its surrogate data.The method is first tested on stochastic processes,the Lorenz,Rossler,Mackey-Glass and high dimensional coupling equations.Then it is applied to two data sets of Santa Fe to test its effect on experimental data.Finally,the robust ness of the method is tested on the time series with different data length and different levels of additive noise.更多还原