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Entropy 2014, 16(7), 3889-3902; doi:10.3390/e16073889
Article

Identifying Chaotic FitzHugh–Nagumo Neurons Using Compressive Sensing

1
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1,2,*  and 3
Received: 4 March 2014 / Revised: 23 June 2014 / Accepted: 7 July 2014 / Published: 15 July 2014
(This article belongs to the Special Issue Information in Dynamical Systems and Complex Systems)
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Abstract

We develop a completely data-driven approach to reconstructing coupled neuronal networks that contain a small subset of chaotic neurons. Such chaotic elements can be the result of parameter shift in their individual dynamical systems and may lead to abnormal functions of the network. To accurately identify the chaotic neurons may thus be necessary and important, for example, applying appropriate controls to bring the network to a normal state. However, due to couplings among the nodes, the measured time series, even from non-chaotic neurons, would appear random, rendering inapplicable traditional nonlinear time-series analysis, such as the delay-coordinate embedding method, which yields information about the global dynamics of the entire network. Our method is based on compressive sensing. In particular, we demonstrate that identifying chaotic elements can be formulated as a general problem of reconstructing the nodal dynamical systems, network connections and all coupling functions, as well as their weights. The working and efficiency of the method are illustrated by using networks of non-identical FitzHugh–Nagumo neurons with randomly-distributed coupling weights.
Keywords: compressive sensing; nonlinear system identification; neuronal networks; chaos; random networks compressive sensing; nonlinear system identification; neuronal networks; chaos; random networks
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Su, R.-Q.; Lai, Y.-C.; Wang, X. Identifying Chaotic FitzHugh–Nagumo Neurons Using Compressive Sensing. Entropy 2014, 16, 3889-3902.

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