Power-law sensitivity to initial conditions in a time series with applications to epileptic seizure detection

Recently, the concept of exponential sensitivity to initial conditions (ESIC) of deterministic chaos is generalized to power-law sensitivity to initial conditions (PSIC). We describe a general computational procedure to examine PSIC from a time series. Study of noise-free and noisy logistic and Henon maps at the edge of chaos finds that PSIC cannot be shown from clean scalar time series. However, when there is dynamic noise, motions around the edges of chaos all collapse onto the PSIC attractor regardless whether they are simply regular or truly chaotic when noise is absent. Hence, dynamic noise makes PSIC observable. The PSIC concept is further applied to the analysis of long continuous EEG signals with epileptic seizures. It is shown that measures from the PSIC framework is quite effective in detecting seizures, often better than the Lyapunov exponent based methods from the conventional ESIC framework.