Investigating Synchronization Phenomena in Complex Networks Consisting of Oscillators
Tsuyoshi ISOZAKI Takumi NARA Yoko UWATE Yoshifumi NISHIO ( Tokushima University)
1. Introduction
Complex networks have attracted a lot of attention.
Some features of complex networks are related to real world networks and have been studied in terms of network struc- ture and interactions between nodes. In this study, we build three network models by using oscillators and investigate synchronization phenomena between nodes in networks.
2. System Model
Figure 1 shows van der Pol oscillator. This oscillator consists of a capacitor, an inductor and a nonlinear element.
Figure 2 shows three network models.
v
i
Li
gC L G
i
Figure 1: van der Pol oscillator.
(a) (b) (c)
Figure 2: Network model.
(a) Regular. (b) ER random. (c) BA scale-free.
Table 1:Node numberN, Average node degreedavg, Max- imum node degreedmaxand Average distanceDavgof three network models.
network Regular ER random BA scale-free
N 100 100 100
davg 4.0 3.88 3.92
dmax 4.0 1.0 2.0
Davg 12.87 3.58 2.98
The normalized circuit equations are described as follows:
dxi
dτ =α {
εxi(1−x2i)−yi−
∑100 i,j=1
γij(xi−xj) }
dyi
dτ =xi
(i, j= 1,2,· · ·,100).
(1)
3. Results
We set the parameters of the system as ε = 0.1 and α= 1.0. Here, the mismatch is added toα. The mismatch is generated by random and the range of the mismatch is set to [-0.5:0.5]. In this study, we focus on the relation between mismatch differences, synchronization rates and coupling strengthγand show the results of simulations in the three network models.
Synchronization rate Synchronization rate
Mismatch differences Mismatch differences
(a)γ=0.5 (b)γ=4.0
Figure 3: The relation between mismatch differences, syn- chronization rates and coupling strengthγ(Regular).
Synchronization rate
Mismatch differences
Synchronization rate
Mismatch differences
(a)γ=0.5 (b)γ=3.0
Figure 4: The relation between mismatch differences, syn- chronization rates and coupling strengthγ(ER random).
Synchronization rate Synchronization rate
Mismatch differences Mismatch differences
(a)γ=0.5 (b)γ=1.2
Figure 5: The relation between mismatch differences, syn- chronization rates and coupling strengthγ(BA scale-free).
As a result, it is not confirmed that synchronization and mismatch differences are heavily related in regular network from Fig. 3. Further it is confirmed that synchronization and mismatch differences are related in ER random and BA scale-free and when coupling strength is higher, pair of nodes of high synchronization rate increase in ER random but pair of nodes of high synchronization rate decrease in BA scale-free from Fig. 4 and Fig. 5.
4. Conclusion
In this study, we have investigated the synchronization in three network models. It was confirmed that the rela- tion between mismatch differences, synchronization rates and coupling strength differs each the network model.
令和2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 (愛媛大学) 2020 SHIKOKU-SECTION JOINT CONVENTION RECORD OF THE INSTITUTES OF ELECTRICAL AND RELATED ENGINEERS (EHIME UNIV.)
