Chaotic Time Series Analysis of Functional Magnetic Resonance Imaging

Time series is a very popular type of data which exists in many practical applications, while recent studies show that chaos theory may be a powerful tool in time series analysis. In this paper, we applied chaotic time series theory to analyze the functional magnetic resonance imaging (fMRI) data. The preprocessing of fMRI data is briefly introduced and the reconstruction of the phase space is expounded. The largest Lyapunov exponent, the Kolmogorov entropy and the correlation dimension were explored on the basis of the fMRI time series with small data sets, second-order correlation entropy and G-P algorithm, respectively. The experiment results indicated that the novel techniques based on chaotic time series, not only can prove the obvious existence of chaotic characteristics in the fMRI data that describes the brain neuronal system, but also provides a new explication for chaotic brain behaviors.