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Detection of chaotic determinism in time series from randomly forced maps.
Physica D: Nonlinear Phenomena ( IF 4 ) Pub Date : 1997-01-01 , DOI: 10.1016/s0167-2789(96)00159-5
K H Chon 1 , J K Kanters , R J Cohen , N H Holstein-Rathlou
Affiliation  

Time series from biological system often display fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". Despite this effort, it has been difficult to establish the presence of chaos in time series from biological sytems. The output from a biological system is probably the result of both its internal dynamics, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes, i.e., a positive characteristic exponent that leads to sensitivity to initial conditions. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

中文翻译:

从随机强制映射中检测时间序列中的混沌确定性。

来自生物系统的时间序列通常会显示测量变量的波动。已经进行了很多努力来确定这种可变性是否反映出确定性的混乱,或者仅仅是“噪声”。尽管做出了这种努力,但很难从生物系统中按时间序列确定混沌的存在。生物系统的输出可能既是其内部动力学的结果,又是来自周围环境对系统的输入的结果。这意味着该系统应被视为具有随机和确定性成分的混合系统。我们提出一种方法,该方法似乎对确定时间序列中是否存在确定性很有用,并且该确定性是否具有混沌属性(即导致对初始条件敏感的正特征指数)是否有用。该方法依赖于将非线性自回归模型拟合到时间序列,然后在观察到的系统状态概率分布上估算模型的特征指数。该方法通过计算机仿真进行测试,并应用于心率变异性数据。
更新日期:2019-11-01
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