Identifying Chaotic FitzHugh–Nagumo Neurons Using Compressive Sensing

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

doi:10.3390/e16073889

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.

Highlights

We address the problem of the data-based identification of a subset of chaotic elements embedded in a network of nonlinear oscillators
We develop a completely data-driven method to detect chaotic elements embedded in a network of nonlinear oscillators, where such elements are assumed to be relatively few
The chaotic elements can be the source of certain diseases, and their accurate identification is desirable

Summary

Introduction

We address the problem of the data-based identification of a subset of chaotic elements embedded in a network of nonlinear oscillators. Given such a network, we assume that time series can be measured from each oscillator. The oscillators, when isolated, are not identical in that their parameters are different, so dynamically, they can be in distinct regimes. Consider the situation where only a small subset of the oscillators are chaotic and the remaining oscillators are in dynamical regimes of regular oscillations. The challenge is to identify the small subset of originally (“truly”) chaotic oscillators

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