Feature Extraction of Neuron Group
Composed of Two Different Firing Patterns
Using Nonlinear Analysis
Yoko Uwate and Yoshifumi Nishio
Dept. of E. E. Eng., Tokushima University
2-1 Minami-Josanjima Tokushima 770-8506 Japan
Email: {uwate, nishio}@ee.tokushima-u.ac.jp

Abstract— In our previous work, feature visualization using nonlinear analysis has been proposed for time series of spike firing
rates of neuronal activity. In this study, we investigate theneuronal activity of two mixed types of neurons: regular spikingand chattering. We investigate the effects of an increased rate of
the number of chattering neurons.

II.

IZHIKEVICH NEURON MODEL

Izhikevich neuron model efficiently produces a wide
variety of neuron spiking and bursting dynamics. TheIzhikevich neuron model is described by the following
equations.

Keywords; neuronal activity, nonlinear time-series analysis

I.

INTRODUCTION

Understanding how brain circuits develop and operate is amajor goal for many neuroscience projects. Burst patterns inneuronal networks may have an important role in information
processing in the brain. Therefore, detecting and analyzing
burst patterns are investigated in various fields. Although it isimportant to study burst patterns in order to understand thecorrelation and communication processes of neurons, unveilinga structure of the whole neuronal network is also required.
On the other hands, nonlinear time-series analysis is a
useful tool for characterizing the dynamics behind the observed
time-series data. The neuronal data obtained from living
neurons should be high-dimensional and dynamic nature. In
such case, nonlinear time-series analysis can be used tocharacterize the neuronal data.

Where v represents the membrane potential of the neuron, urepresents a slow membrane recovery variable, accounting forthe activation of K+ ion currents and inactivation of Na+ ioncurrents. Iex denotes the excitatory input current. In thecomputer simulations, 100 neurons were coupled randomly
with the coupling probability p. The ratio of excitability andinhibitory neuron is 0.8 and 0.2, respectively.
Figure 1 shows the two different firing patterns. Fig. 1 (a)shows regular spiking and Fig. 1 (b) shows chattering. We
investigate the effects of an increased rate of the number ofchattering neurons.

Previously, we proposed the method of feature extraction ofneuronal activity using nonlinear time series analysis [1]. We
also investigated attractor reconstructions obtained from timeseries data of spike rate [2]. By using the simulations, weconfirmed that the attractor of the network with highconnectivity is larger size than the network with lowconnectivity. However, the complexity of attractor of networkwith low connectivity is higher than the network with highconnectivity. In such simulations, only one firing pattern isused. In the real brain networks, there are several types offiring patterns.

(a) Regular spiking.

In this study, we investigate feature of neuron groupcomposed of two different firing patterns using nonlinearanalysis. We confirm that the neuronal activity with high ratioof chattering has high spike rate in the whole network.

(b) Chattering.
Fig. 1. Two different firing patterns.

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III.

SIMULATION RESULTS

The simulation results are shown in below subsections.
A. Spike Rate
Figure 2 shows the spike rate which is calculated the spiketimes during a certain bin by changing the ratio of chattering
neurons. By increasing the ratio of chattering neurons, the peakof spike rate becomes large.
spike rate (Hz)300
"hindo_RS100.dat"

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t(c) Chattering neurons: 70%.
Fig. 2. Spike rate time series.
B. Attractor reconstruction
The attractor of dynamical systems can be reconstructed
topologically in the embedding space from Takens' theorem[3].
Figure 3 shows the simulation results when neuronal timeseries data is embedded in 3-dimensional space with time delay
10. From these figures, we confirm that the size of attractor ofchattering neuron 70% is largest than the others. However, noinformation other than the size of the attractor can beunderstood from these results. We need to investigate thecomplexity of the attractors by using Poincare section.
IV.

CONCLUSIONS

We investigated feature of neuron group composed of two
different firing patterns using attractor reconstruction as
nonlinear analysis. We confirm that the neuronal activity withhigh ratio of chattering has large size of attractor.
In the future works, we would like to analyze the spike rate
time series using other nonlinear techniques in order tounderstand the characteristics of neuronal activity in moredetailed.

979-8-3503-2703-8/23/$31.00 ©2023 IEEE(c) Chattering neurons: 70%.
Fig. 3. Attractor reconstruction.
REFERENCES[1]

Y. Uwate, M. E. J. Obien, U. Frey and Y. Nishio, “Time Series Analysis
of Neurons and Visualization of Network Characteristics”, Proc. ofNCSP’19, 2019.

[2]

Y. Uwate, M. E. J. Obien, U. Frey and Y. Nishio, “Modeling of Bursting
Neurons and Its Characteristic using Nonlinear Time Series Analysis”,
Proc. of NCSP’20, March, 2020.

[3]

F. Takens, “Detecting Strange Attractors in Turbulence,” In D.A. Randand B.-S. Young, editors, Dynamical Systems and Turbulence, vol. 898
of Lecture Notes in Mathematics, pp. 366–381, Warwick 1980, 1981.

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