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
 [1] Lambertus A. Peletier, Xi-Ling Jiang, Snehal Samant, Stephan Schmidt. Analysis of a complex physiology-directed model for inhibition of platelet aggregation by clopidogrel. Discrete & Continuous Dynamical Systems, 2017, 37 (2) : 945-961. doi: 10.3934/dcds.2017039 [2] Annalisa Pascarella, Alberto Sorrentino, Cristina Campi, Michele Piana. Particle filtering, beamforming and multiple signal classification for the analysis of magnetoencephalography time series: a comparison of algorithms. Inverse Problems & Imaging, 2010, 4 (1) : 169-190. doi: 10.3934/ipi.2010.4.169 [3] Vera Ignatenko. Homoclinic and stable periodic solutions for differential delay equations from physiology. Discrete & Continuous Dynamical Systems, 2018, 38 (7) : 3637-3661. doi: 10.3934/dcds.2018157 [4] Christopher Oballe, Alan Cherne, Dave Boothe, Scott Kerick, Piotr J. Franaszczuk, Vasileios Maroulas. Bayesian topological signal processing. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021084 [5] Asim Aziz, Wasim Jamshed, Yasir Ali, Moniba Shams. Heat transfer and entropy analysis of Maxwell hybrid nanofluid including effects of inclined magnetic field, Joule heating and thermal radiation. Discrete & Continuous Dynamical Systems - S, 2020, 13 (10) : 2667-2690. doi: 10.3934/dcdss.2020142 [6] Jakub Kantner, Michal Beneš. Mathematical model of signal propagation in excitable media. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 935-951. doi: 10.3934/dcdss.2020382 [7] Lingchen Kong, Naihua Xiu, Guokai Liu. Partial $S$-goodness for partially sparse signal recovery. Numerical Algebra, Control & Optimization, 2014, 4 (1) : 25-38. doi: 10.3934/naco.2014.4.25 [8] Björn Popilka, Simon Setzer, Gabriele Steidl. Signal recovery from incomplete measurements in the presence of outliers. Inverse Problems & Imaging, 2007, 1 (4) : 661-672. doi: 10.3934/ipi.2007.1.661 [9] Wei Xu, Liying Yu, Gui-Hua Lin, Zhi Guo Feng. Optimal switching signal design with a cost on switching action. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2531-2549. doi: 10.3934/jimo.2019068 [10] Marcel Freitag. The fast signal diffusion limit in nonlinear chemotaxis systems. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1109-1128. doi: 10.3934/dcdsb.2019211 [11] Michael Brandenbursky, Michał Marcinkowski. Entropy and quasimorphisms. Journal of Modern Dynamics, 2019, 15: 143-163. doi: 10.3934/jmd.2019017 [12] Wenxiang Sun, Cheng Zhang. Zero entropy versus infinite entropy. Discrete & Continuous Dynamical Systems, 2011, 30 (4) : 1237-1242. doi: 10.3934/dcds.2011.30.1237 [13] Yixiao Qiao, Xiaoyao Zhou. Zero sequence entropy and entropy dimension. Discrete & Continuous Dynamical Systems, 2017, 37 (1) : 435-448. doi: 10.3934/dcds.2017018 [14] José M. Amigó, Karsten Keller, Valentina A. Unakafova. On entropy, entropy-like quantities, and applications. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3301-3343. doi: 10.3934/dcdsb.2015.20.3301 [15] Ping Huang, Ercai Chen, Chenwei Wang. Entropy formulae of conditional entropy in mean metrics. Discrete & Continuous Dynamical Systems, 2018, 38 (10) : 5129-5144. doi: 10.3934/dcds.2018226 [16] François Blanchard, Wen Huang. Entropy sets, weakly mixing sets and entropy capacity. Discrete & Continuous Dynamical Systems, 2008, 20 (2) : 275-311. doi: 10.3934/dcds.2008.20.275 [17] Pan Zheng. Asymptotic stability in a chemotaxis-competition system with indirect signal production. Discrete & Continuous Dynamical Systems, 2021, 41 (3) : 1207-1223. doi: 10.3934/dcds.2020315 [18] Mengyao Ding, Wei Wang. Global boundedness in a quasilinear fully parabolic chemotaxis system with indirect signal production. Discrete & Continuous Dynamical Systems - B, 2019, 24 (9) : 4665-4684. doi: 10.3934/dcdsb.2018328 [19] Yuanjia Ma. The optimization algorithm for blind processing of high frequency signal of capacitive sensor. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1399-1412. doi: 10.3934/dcdss.2019096 [20] Hai-Yang Jin, Zhi-An Wang. The Keller-Segel system with logistic growth and signal-dependent motility. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3023-3041. doi: 10.3934/dcdsb.2020218

2018 Impact Factor: 1.313

Metrics

• PDF downloads (63)
• HTML views (0)
• Cited by (17)

Other articlesby authors

• on AIMS
• on Google Scholar

[Back to Top]