Identifying Chaotic FitzHugh–Nagumo Neurons Using Compressive Sensing

Ri-Qi Su, Ying-Cheng Lai, Xiao Wang

Research output: Contribution to journalArticle

6 Citations (Scopus)
4 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)3889-3902
Number of pages14
JournalEntropy
Volume16
Issue number7
DOIs
Publication statusPublished - 15 Jul 2014

Fingerprint

neurons
dynamical systems
time series analysis
embedding
set theory
shift

Keywords

  • compressive sensing
  • nonlinear system identification
  • neuronal networks
  • chaos
  • random networks

Cite this

Identifying Chaotic FitzHugh–Nagumo Neurons Using Compressive Sensing. / Su, Ri-Qi; Lai, Ying-Cheng; Wang, Xiao.

In: Entropy, Vol. 16, No. 7, 15.07.2014, p. 3889-3902.

Research output: Contribution to journalArticle

Su, Ri-Qi ; Lai, Ying-Cheng ; Wang, Xiao. / Identifying Chaotic FitzHugh–Nagumo Neurons Using Compressive Sensing. In: Entropy. 2014 ; Vol. 16, No. 7. pp. 3889-3902.
@article{6a4dd6edebdd49e59d8c86ca1117275d,
title = "Identifying Chaotic FitzHugh–Nagumo Neurons Using Compressive Sensing",
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 toabnormal functions of the network. To accurately identify the chaotic neurons may thus be necessary and important, for example, applying appropriate controls to bring the networkto 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 canbe 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 efficiencyof 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",
author = "Ri-Qi Su and Ying-Cheng Lai and Xiao Wang",
note = "Date of Acceptance: 07/07/2014",
year = "2014",
month = "7",
day = "15",
doi = "10.3390/e16073889",
language = "English",
volume = "16",
pages = "3889--3902",
journal = "Entropy",
issn = "1099-4300",
publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",
number = "7",

}

TY - JOUR

T1 - Identifying Chaotic FitzHugh–Nagumo Neurons Using Compressive Sensing

AU - Su, Ri-Qi

AU - Lai, Ying-Cheng

AU - Wang, Xiao

N1 - Date of Acceptance: 07/07/2014

PY - 2014/7/15

Y1 - 2014/7/15

N2 - 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 toabnormal functions of the network. To accurately identify the chaotic neurons may thus be necessary and important, for example, applying appropriate controls to bring the networkto 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 canbe 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 efficiencyof the method are illustrated by using networks of non-identical FitzHugh–Nagumo neurons with randomly-distributed coupling weights.

AB - 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 toabnormal functions of the network. To accurately identify the chaotic neurons may thus be necessary and important, for example, applying appropriate controls to bring the networkto 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 canbe 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 efficiencyof the method are illustrated by using networks of non-identical FitzHugh–Nagumo neurons with randomly-distributed coupling weights.

KW - compressive sensing

KW - nonlinear system identification

KW - neuronal networks

KW - chaos

KW - random networks

U2 - 10.3390/e16073889

DO - 10.3390/e16073889

M3 - Article

VL - 16

SP - 3889

EP - 3902

JO - Entropy

JF - Entropy

SN - 1099-4300

IS - 7

ER -