平成 28 年度電気関係学会四国支部連合大会 講演論文集 (2016 徳島大学)
2016 SHIKOKU-SECTION JOINT CONVENTION RECORD OF THE INSTITUTES OF ELECTRICAL AND RELATED ENGINEERS (TOKUSHIMA)

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Neural Firing of Coupled Izhikevich Neurons with Bug Neuron
Ryota OSHIMA

Yoko UWATE
Yoshifumi NISHIO( Tokushima University)

1. Introduction

Furthermore, we investigate the eﬀect of neurons when thecoupling strengths δ between neurons are fixed as samevalue. Range of δ is set from 0 to 0.8, the bug occurs atthe rate of 10 - 50%. The bug is defined as the phenomenon
that causes abnormal at the time of the neural firing. In
particular, neuron including a bug does not fire even when
the threshold value is exceeded.

Myriad of neurons exist in our brain. Information processing and transmission are performed by neural firing. In
analyzing the neural firing, it is essential to consider thecycle of neural firing and firing pattern.
In this study, we focus on the influence that the neuron
including a bug has on others neurons. Furthermore, weinvestigate the phenomena when the neurons are coupled as
the ladder network. By carrying out computer simulations,the propagation of the bug is confirmed.

2. System model
Figure 2: Model of the ladder network.

The Izhikevich neuron model [1] is presented that reproduces spiking and bursting behavior of known types of cortical neurons as shown in Fig. 1.

3. Simulation results
Figure 3 shows some of simulation results. As some simulation results, propagation of the bug is observed. In thecase of pattern 1, the bug is propagated to all neurons on
the network. However, the bug is propagated only neurons
adjacent to the bug neuron for pattern 2.
In addition, we observed various firing patterns. Twicefiring per one cycle is observed as one case.

Figure 1: Examples of neural firing patterns.
In addition, this model is described by the following equations: v̇ = 0.04v 2 + 5v + 140 − u + I(1)u̇ = a(bv − u),with the auxiliary after-spike resetting
if v ≥ 30mv, thenFigure 3:

Time waveforms when we set the couplingstrength δ = 0.8 and bug rate = 50%.

 v←c(2)

4. Conclusionsu ← u + d.

In this study, we have investigated the eﬀect of neuron
including a bug on the network. As some computer simulations, we have confirmed the propagation of the bug in aladder network. In addition, the firing patterns of each neurons are changed by coupling the neuron including a bug.
In our future works, we would like to simulate for large
scale and investigate by the combination of other firing patterns.

Here, v and u are dimensionless variables, and a, b, c andd are dimensionless parameters and ˙ = d/dt, where t represents the time. The variable v represents the membranepotential of the neuron and u represents a membrane recovery variable. In this study, we consider ladder network
using Izhikevich neuron model as shown in Fig. 2. We set
the neuron including a bug to neuron 2. These neurons arecoupled by a gap junction and they are fixed as same typeof neuron. We investigate two patterns which are describedas follows:

Reference[1] Eugene M. Izhikevich, “Simple Model of Spiking
Neurons,” IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 14, NO. 6, NOVEMBER 2003.

• Pattern 1 : Regular Spiking (RS).
• Pattern 2 : Chattering (CH).

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