令和3年度 電気・電子・情報関係学会 四国支部連合大会 講演論文集
2021 Shikoku-Section Joint Convention Record of the Institutes of Electrical and Related Engineers

1-23
Investigating Relationship between Synchronization Phenomenaand Complex Network Properities by Using Chaotic Circuits
Sohei SHIMA

Tsuyoshi ISOZAKI Yoko UWATE( Tokushima University)

1. Introduction
Synchronous phenomena like a frog chorus and a
metronome can be observed in various parts of our lives. In
this study, we focus on the synchronization of chaotic circuits. We investigate the synchronization rate from chaotic
circuits connected in the network. In order to make the connection as similar as possible to a real network, three kindsof complex networks with diﬀerent properties are used.

2. System Model
Figure 1 shows the chaotic circuit used in this study.
The diﬀerence between the two chaotic circuits is whether
dual-directional diodes or one-directional diode. The three
network models are shown in Fig. 2. Network properties ofthree models are shown in Tab. 1.

(a)Dual-directional diode.

(b)One-directional diode.

Figure 1: Chaotic circuits.

Yoshifumi NISHIO

where the function f (yi ) is the equation for the diode anddescribed as follows:f (yi ) =12f (yi ) =12(yi +

1
1− yi −
δδyi +

1
1− yi −
δδ().

(2).

(3))

The Eq. (2) shows the characteristic equation of dualdirectional diodes and the Eq. (3) shows one-directional
diode.

3. Results
The parameters of the system are set to α = 0.412, β =3.0 and δ = 470 for dual-directional diodes, δ = 9.0 for onedirectional diode. Here the initial values x, y, and z aregenerated in two diﬀerent methods: regular and random
and the ranges of the initial values are set to [0.1 : 0.2]. In
this study, we focus on the relation between initial values
diﬀerences, synchronization rates and network properities.
Tables 2 and 3 show the simulation results in the three
network models. Further we investigate the synchronization
rates by changing the coupling strength. The BA model isexcluded from the comparison because a suﬃcient numberof measurements cannot be obtained due to its properties.

Table 2: Synchronization rates (dual-directional diodes).

(a)

(b)

MethodRegularRandom(c)MethodRegularRandomfree. (b) ER random. (c) WS Regular.

Table 1: Network properties of three models (Node numberNetworkBA scale-freeER random

WS RegularN50
1.96
143.935

50
2.2
5.0
5.662

50
2.0
2.0
12.755

davg
dmax
Davg

∑


γij (zi − zj ).
 z˙i = −xi − βyi −
50

i,j=1

WS[%]
30.3
29.8

BA[%]
(73.8)(79.9)

ER[%]
90.1
87.9

WS[%]
72.9
82.3

From Tabs. 2 and 3, the synchronization rates are highfor one-directional diode. Further, it is confirmed that theER model has relatively high synchronization rates and therates are not obtained when coupling strength is increasedin BA model.

4. Conclusion

The normalized circuit equations are given as follows:x˙i = αxi + zi
 y˙i = zi − f (yi )

ER[%]
35.4
34.1

Table 3: Synchronization rates (one-directional diode).

Figure 2: Complex network models (N =50). (a) BA scale-

N , Average node degree davg , Maximum node degree dmax
and Average distance Davg ).

BA[%](35.5)(35.6)(1)

In this study, it was considered that high synchronizationrates could be obtained for network topology with small
average distances. However, in the BA model of the circuit with high degree nodes, the high synchronization rates
could not be obtained because the circuit would be heavily
loaded and the circuit would not oscillate. There was no relationship between the way of the initial values were given
and the synchronization rates.

–23–