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)

1-14Synchronization in Complex Networks of Parametrically
Excited Oscillators with Parameter Mismatch
Kosuke Oi

Yoko UWATE
Yoshifumi NISHIO(Tokushima University)

1. Introduction

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In this study, in order to research the relationship between
the structural metrics in subset of the nodes including larger
mismatch and synchronization in complex network, we investigate synchronization in complex network by adding large
mismatch in three nodes. These nodes are elected by thevalue of structural metrics (degree and path length) in complex network. First, we investigate the synchronization probability in the network by changing the degree of the threenodes added larger mismatch. Next, we investigate the synchronization probability in the network by changing the path
length among hubs, three nodes with larger mismatch.

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3545262714613223(a) The location of the 5color nodes with larger mis- (b) Synchronization probability.
match M .

Figure 2: The location of the 5-color nodes and synchronization
probability.

2. System model
The circuit model of parametrically excited oscillator isshown in Fig. 1 (a). Complex network model is shown inFig. 1. (a). In Fig. 1. (a), n express the circuit number ofthe complex network is shown in Fig. 1 (b).
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3bility (case 2).

5462433185576202810(a) Circuit model.

4850354511292ity (case 1).

171 2149(a) Synchronization probabil- (b) Synchronization proba-

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184233262714613223(b) Complex network model.

Figure 1: System model.
The normalized circuit equations of this circuit equations are
given by the following equations.

 dxn

 dτ

 dyndτ=ε(xn − x3n ) − yn + δ∑k∈Sn=1xnγ(τ )(c) Synchronization probability (case 3).

Figure 3: The synchronization probability in 3 cases.

(xk − xn )(1)

where n = 1, 2, 3, ..., 10. Sn is the set of nodes which are
directly connected to the node n.

3. Simulation results
In this simulation, we investigate the synchronization
probability in complex network by change the value of mismatch M from 0.002 to 0.01.
First, we add the M in three nodes which have the 5 types
degrees (1 to 5). Figure 2 (a) shows the 5 types nodes withthe value of mismatch M , and these colors are corresponding to the number of degree in Fig. (2) (b).When three nodes
have 4 degrees, we can confirm the synchronization probability maintains the highest condition. On the other hand,when three nodes have 1, we can confirm the synchronization
probability maintains the lowest condition.
Next, we investigate in what way the synchronization
probability in complex network draw influence from the path
length among hubs and three nodes with larger mismatch M .
We investigate this influence in 3 cases. The results of thisinvestigation are shown in Fig. (3). In the case 1, we investigate the passage of the synchronization probability bychanging larger mismatch M and the path length between
hubs and each of three nodes with M . In the case 2, thehubs (15th and 58th node) are not connected to any of threenodes with M . Based on the acknowledgment, we investigate
the passage of the synchronization probability by changing
larger mismatch M and the path length among each of threenodes with M . In the case 3, the hubs (15th or 58th node)
are connected to any of three nodes with M . On that basis,
we investigate the passage of the synchronization probability
by changing larger mismatch M and the path length among
each of three nodes with M .

4. Conclusions
In this study, in order to more particular investigationof synchronization in complex network, we investigated synchronization probability in complex network by changing
structural metrics (degree and path length) of the nodes corresponding to the subset of the nodes adding larger mismatch
than other nodes.
We could observe the various change of the synchronization probability by changing structural metrics.

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