令和元年度電気関係学会四国⽀部連合⼤会 講演論⽂集 (2019 新居浜⾼専)
2019 SHIKOKU-SECTION JOINT CONVENTION RECORD OF THE INSTITUTES OF ELECTRICAL AND RELATED ENGINEERS (NIIHAMA)

1-11Synchronization Phenomena
in Coupled Chaotic Circuits with Coupling Strength
Depending on Number of Links
Kyohei FUJII

Yoko UWATE Yoshifumi NISHIO( Tokushima University)

1. Introduction

3. Simulation results

In our living life, complex network can be seen in various fields. Synchronization phenomena observed in complex
network have been investigated by many researchers. Thereare various investigations of synchronization using chaoticcircuits.
In this study, we focus on indirect connection and coupling strength of coupled chaotic circuit network. Indirect
coupling refers to a connection through multiple circuits.
We set coupling strength depending the number of links.
The network has scale free property.

We investigate synchronization of CC18-CC19 when wechange each coupling strength. Some link is multiplied magnification. We confirm synchronization when other links
change synchronization of CC18-CC19. This link basicallyhas about 80% synchronization rate. When synchronization
rate reaches 50% to 70%, we judge that synchronization ischanged. In Fig. 3, we represent some links. There arevarious types of these links. We choose indirect link, links
with indirect and strong coupling strength, links far from
CC18-CC19.

2. System model
The chaotic circuit model is shown in Fig. 1. Figure 2 isnetwork to used in this study. The point which constitutethe network is called node and the lines connecting nodes
are called links. Nodes having many links are called hubs.

Figure 3: Synchronization rate of chosen links.
When some links of coupling strength are extremely
weak, synchronization of CC18-CC19 is weakened. Next,
we calculate magnification one by one for all links and investigate synchronization rate. Figure 4, we checked judgedlinks.

Figure 1: Circuit model.

Figure 2: Network model.

Normalized circuit equations of the coupled chaotic circuits are as follows: dx

= zn ,
dτ




 dy

= αγyn − αf (yn − zn ) − αδnmdτ




dz


 dτ = f (yn − zn ) − xn .

∑(yn − ym ),(1)m∈Sn

Figure 4: Judged links in network.
In this result, when some links open or extremely
weaken the coupling strength, synchronization of far links
is weaken.

In this equation, δ denotes the coupling strength. Sn
is a set of nodes which are connected to CCn. We define
synchronization as Eq. (2). Synchronization rate is ratio of
number of synchronization to all calculate point.
|yn − ym | < 0.03

(n, m = 1, 2, · · ·, 20)

4. Conclusion
In this study, we have investigated the influence of indirectry coupling by using a scale-free coupled chaotic network with changing the couplings strength. We compare some synchronization when the coupling strength waschanged some values.
In this result, we found that the strength of synchronization is diﬀerent even with the same coupling strength. We
could not clarify the reason in this study. We must compare this result with other result. Next, we focus other links
which have similar terms and simulate in the same way.

(2)

We decide coupling strength value based on the diﬀerenceof links. The value of coupling strength is determined bydegree of the node using Eq. (3).
δnm =1.0
1.0 + u(3)We set that u is diﬀerence of degree between two nodes.

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