多目标优化方法检测随机受迫系统的混沌现象以及在心率变异信号分析中的应用

USING MULTI-OBJECTIVE OPTIMIZATION ALGORITHM TO DETECT CHAOTIC DETERMINISM IN TIMES SERIES FROM RANDOMLY FORCED MAPS AND ITS APPLICATIONS TO HEART RATE VARIABILITY

心率变异信号往往很不规则 ,确定它是混沌还是噪声是目前研究的焦点。从非线性动力学的角度 ,虽然已进行了大量的工作 ,但迄今还没有明确的证据表明心率变异信号是混沌的。本文假设心率变异信号是其内在动力学机制和外部环境影响混合的产物 ,并提出一种多目标优化方法 ,以此获得一组既与心率变异信号尽可能接近又对于某种非线性动力学系统为确定的序列 ,然后计算依赖于初始值敏感的特征指数 ,定量刻划系统中确定性因素的动力学特性。在成功地检验了两类受迫混沌模型后 ,应用于心率变异信号分析 ,结果表明

Time series generated from biological systems alwuys display flnctions in the measured variables. Much effort had been directed at determining whether this variability reflected deterministic chaos, or whether it was merely 'noise'. Despite this effort, it had been difficult to establish the process of chaos in time series from biological systems. The output from such a system was probably the result of both its internal dynamics, and the input to the system from surroundings. This implied that the system should be viewed as a mixed system with both stochastic and deterministic components. We presented a multi objective optimization algorithm to find a time series that was as close as possible to the heart rate variability signals subjected to the constraint that it be deterministic with respect to some dynamics. If the determinism had chaotic attributes, i.e, a positive characteristic exponent that led to sensitivity to initial conditions. The method was tested by computer simulations, and applied to heart rate variability data. We found that the deterministic components of heart rate variability were chaotic.