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)

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Ratio of Chaotic Propagation in Scale Free Networkby Changing Clustering Coeﬃcient
Takahiro CHIKAZAWA
Yoko UWATE( Tokushima University)

Yoshifumi NISHIO

1. Introduction

3. Simulation results

In this study, in order to research the spread of chaotic
behavior in various complex networks, we investigate theratio of chaotic propagation in scale-free network with coupled chaotic circuits. The scale-free network is composed ofcoupled chaotic circuits when one circuit is set to generatechaotic attractor and the other circuits are set to generate
three-periodic attractors. By using computer simulations,
we investigate the ratio of propagation by changing the initial chaos position. Moreover, the initial position of chaotic
attractor changes according to the clustering coeﬃcient ineach node.

We investigate the ratio of chaotic propagation in proposed system model. First, in the initial state of each node,
one circuit is set to generate chaotic attractor and the othercircuits are set to generate three-periodic attractors. Next,
we change the initial chaos position according to the clustering coeﬃcient C.
Figure 3 shows the simulation results of ratio of propagation according to clustering coeﬃcient in each node. For
example, in Fig. 3, when the clustering coeﬃcient C in theinitial chaos position is 0.044, we set the chaotic attractor
in 15th node. Also, when the clustering coeﬃcient C in theinitial chaos position is 1.000, we set the chaotic attractor
in 23th, 46th or 47th node. In addition, we investigate theratio of propagation in the static state when we fix couplingstrength as γ = 0.001, 0.005.

2. Proposed method
The chaotic circuit is shown in Fig. 1. This circuit
consists of a negative resistor, two inductors, a capacitorand dual-directional diodes. This chaotic circuit is called
Nishio-Inaba circuit.
Figures 2 shows the proposed scale-free network. In our
proposed network model, each chaotic circuit is coupled by
one resistor R. Moreover, proposed system model uses 49
coupled chaotic circuits and 84 edges.
5i2i134

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17333837

L1-rC

L2v

4939vdCn

44284347

Figure 1: Chaotic circuit.

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421913612188212426715222741631

4146

20324048

1410932111232545

Figure 2: System model.

Topological structures in complex networks of N nodes
and E edges can be evaluated by the typical three types
structural metrics (degree, path length and clustering coeﬃcient). First, degree (k) is the number of edges whichis connected on a node. Second, path length(L) shows theshortest path in the network between two nodes. Third,
clustering coeﬃcient (C) shows the number of actual links
between neighbors of a node divided by the number of possible links between those neighbors. These are given asfollows;
L=N −1N! !
2l(m, n).
N (N − 1)

Figure 3: Ratio of chaotic propagation according to clustering coeﬃcient in each node.
From the result, as the coupling strength become larger,
the three-periodic attractors are easily aﬀected from thechaotic attractor in each initial chaos position. Moreover, as
the clustering coeﬃcient in the initial chaos position becomelarger, the chaos propagation become to more easy.

4. Conclusions(1)

In this study, we have investigated the ratio of chaotic
propagation by changing the initial chaos position according to clustering coeﬃcient. By the computer simulations,
we confirmed that the three-periodic attractors are aﬀectedfrom the chaotic attractors when the coupling strength increases. From the above results, we confirm that ratio ofpropagation in scale-free network is easily aﬀected from thechaotic behavior by increasing clustering coeﬃcient.

m=1 n=m+1

C=1 !
1 !
2En
Cn =.
NN
kn (kn − 1)
NN

n=1

n=1

(2)

Furthermore, average degree is 2.720, average path lengthis 3.503 and average clustering coeﬃcient is 0.112 in the
proposed system model.

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