Neural Network Criterion And Its Application In The Pseudoperiodic Dynamic Detection

Nonlinear science has been rapidly developing during the past years. For the nonlinear systems which cannot build mathematics models directly, we can get nonlinear time series by experiments or observations. We usually wish to understand the underlying dynamics hidden under these time series. In this paper, we focus on the pseudoperiodic time series dynamic detection.Traditional methods, usually relaying on the estimation of nonlinear invariants such as correction dimension, Lyapunov exponent or distraction dimension, sometimes, are unreliable. It has been proved that the filtered noise can mimic low-dimensional chaotic attractors. Later, the surrogate method gives a new path for time series dynamic detection, however,it is not suitable for pseudoperiodic time series, because the presence of strong periodicity tends to mask other deterministic behavior hidden in the time series.We find that the figure of neural network weight distribution usually exhibits the underlying dynamica hidden in the pseudoperiodic time series through lots of the simulation data experiments. So we propose the weight distribution criterion for pseudoperiodic data dynamic detection. By analysising the Levenberg-marquart(LM) training process, we get the connection between the final weight distribution and the training data. Its proves the weight distribution criterion in theroy aspect. At the same time, we analysis the robust of the weight distribution criterion by the simulation data generating form the partional equation. As application, we employ our method to human ECG and normal vowels datas for chaos detection. At the end of this paper, we propose two retifying direction of our method for improving the correction in pseudoperiodic times series dyanmica detection.