# American Institute of Mathematical Sciences

2009, 6(1): 1-25. doi: 10.3934/mbe.2009.6.1

## Control entropy: A complexity measure for nonstationary signals

 1 Clarkson University, P.O. Box 5815, Potsdam, NY 13699-5815, United States, United States 2 Health Prom and Human Perf, 318 Porter Bldg, Ypsilanti, MI 48197, United States

Received  March 2008 Revised  June 2008 Published  December 2008

We propose an entropy statistic designed to assess the behavior of slowly varying parameters of real systems. Based on correlation entropy, the method uses symbol dynamics and analysis of increments to achieve sufficient recurrence in a short time series to enable entropy measurements on small data sets. We analyze entropy along a moving window of a time series, the entropy statistic tracking the behavior of slow variables of the data series. We employ the technique against several physiological time series to illustrate its utility in characterizing the constraints on a physiological time series. We propose that changes in the entropy of measured physiological signal (e.g. power output) during dynamic exercise will indicate changes in underlying constraint of the system of interest. This is compelling because CE may serve as a non-invasive, objective means of determining physiological stress under non-steady state conditions such as competition or acute clinical pathologies. If so, CE could serve as a valuable tool for dynamically monitoring health status in a wide range of non-stationary systems.
Citation: Erik M. Bollt, Joseph D. Skufca, Stephen J . McGregor. Control entropy: A complexity measure for nonstationary signals. Mathematical Biosciences & Engineering, 2009, 6 (1) : 1-25. doi: 10.3934/mbe.2009.6.1
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