平成 29 年度電気関係学会四国支部連合大会 講演論文集 (2017 愛媛大学)
2017 SHIKOKU-SECTION JOINT CONVENTION RECORD OF THE INSTITUTES OF ELECTRICAL AND RELATED ENGINEERS (EHIME)

1-11
Synchronization Phenomena of Coupled Chaotic Circuits Network withDistance-Dependent Coupling Strength
Kyohei FUJII

Shuhei HASHIMOTO Yoko UWATE( Tokushima University)

Yoshifumi NISHIO

1. Introduction
Modern phenomena and society can be expressed using
the network. The occurrence of synchronization in the network has merit and demerit. When the synchronization rate
is high in the network, the propagation of information andthe likes is carried out quickly. However, there is a harmful
eﬀect that computer virus and infectious diseases and anyother adverse eﬀect.
In this study, we investigate how the synchronization
changes when the coupling strength between the circuits ischanged by distance, and how the synchronization changes
depending on the position of the hub in the network.

Figure 3: Definition of length.

Table 1: Coupling strength.
LinkCStr

2. System Model
The chaotic circuit model is shown in Fig. 1. Furthermore, the network model which we used in this study isshown in Fig. 2. The point that constitutes the network iscalled a node and the lines connecting them are called links.
Nodes with many of these links are called hubs.

A
1.000

B
0.145

C0.055

D0.032

E0.0293. Simulation results
In this study, we set the coupling strength A to E multiplied by 0.14. Tables 2 and 3 show the simulation results of the synchronization rate in method A and method
B. “Link” means which link is to be referred. For example, “CC1-CC2” link is 1-2. “SRate” is the synchronization
rate.

Table 2: Synchronization rate in method A.
LinkSRate[%]
Link
SRate[%]

Figure 1: Circuit model.

dτ= zi −

211yi +− yi −γγ

LinkSRate[%]
LinkSRate[%]

dτ,

1-4
152-6
71-5
62-7
26

1-6
86-9
11

1-7
26
7-8
41

1-8
25
8-10
26

2-1
41
9-10
41

1-2
44
2-4
14

1-3
37
2-5
6

1-4
152-6
7

1-5
62-7
26

1-6
8
6-9
11

1-7
26
7-8
41

1-8
25
8-10
26

2-1
41
9-10
41

As shown in Table 2, when the coupling strength becomes
weaker, the synchronization rate is small. However, thesynchronization rate between hubs remain strong even if
the coupling strength has weak value.

)N∑dziδij (zi − zj ),= −xi − βyi −


1-3
37
2-5
6Table 3: Synchronization rate in method B.

Figure 2: Network model.

Normalized circuit equations of coupled chaotic circuits
are as follows: dxi

= αxi + zi ,

dτ

(
 dyi
1

1-2
44
2-4
14(1)

3. Conclusion
In this study, we investigated how the synchronization
rate changes due to the distance. And, the synchronizationrate changes due to the position of the hub in the network.
In this result, the synchronization rate becomes lower inthe case of the far link where the coupling strength becomes
weak. However, the synchronization rate is high between
the hubs even if the coupling strength has weak value. So,
we need to investigate the relationship between the couplingstrength and number of links.

k∈Cnwhere Cn is set of nodes which are connected to CCn.
Figure 3 shows all length of the edge and name A to E.
Table 1 shows the coupling strength when the shortest link’scoupling strength is 1,000. “CStr” is the coupling strength.
In this study, Method A is a state in which the arrangementof Fig. 2 is not changed. Method B is a state in which CC2and CC6 are exchanged from the state of Fig. 2.

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