平成 27 年度電気関係学会四国支部連合大会 講演論文集 (2015 高知工科大学)
2015 SHIKOKU-SECTION JOINT CONVENTION RECORD OF THE INSTITUTES OF ELECTRICAL AND RELATED ENGINEERS (KOCHI)

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Layout of Cells for CNN Using Three Kindsof Cloning Templates
Mana Tanaka1 ,Yasuteru Hosokawa2 , Yoko Uwate1 , Yoshifumi Nishio1( Tokushima University, 2 Shikoku University)
1

Cell α and Cell β, Cell α and Cell γ, Cell β and Cell γ, Cellα and Cell α, Cell α and Cell β or Cell γ, respectively.

1. Introduction
Cellular Neural Networks (CNNs) using three cells cangenerate double scroll type attractors. In our previous study,
CNN using three kinds of cloning templates was proposed
as one of chaotic oscillatory system. Various phenomena
can be observed. However, relationship between diﬀerences of observed phenomena and the number of cells could
not be revealed. This system to share the elements of the oscillation. Because this system share the elements of oscillation. Therefore, parameters include various the elementsof oscillation in this system. In this study, new system isproposed. This system that cells layout method is changed.
Parameters can divide into various elements in this system.
Phenomena of previous system and new system are compared.

3. Simulation
Figure 1 shows computer simulation of case of six cells(M = 2, N = 3) in previous system. By changing a parameter, some periodic orbits, bifurcation phenomena andchaotic phenomena are observed. However, observed phenomena are not controlled by changing parameter when thenumber of cells are increased. Figure 2 shows computer
simulation of case of one hundred cells (M = 10, N = 10)
in new system. Chaotic phenomena are observed. And thisphenomena can be observed in wide range of parameters ascompared to the previous system.

2. CNN Using Three Kinds of Cloning Templates
The system consists of three kinds of cells which names
are Cell α, Cell β or Cell γ. The diﬀerence of three kindsof cells is only values of cloning templates. The numberof cells is defined as M × N. Cells are coupled as triangle
lattice. The boundary condition is set as a periodic condition. Namely, this system has a torus structure. Structuresof previous and new CNN using three kinds of cloning templates are shown in Table 1. Cloning template parametersof previous system and new system are set as follows.

Previous systemj:αc(1,2)c(1,3)

c(1,N)c(1,1)c(2,2)

c(2,3)

c(3,1)

c(3,2)

c(2,N)c(3,3)β(1,2)
γ(1,3)1γ(2,1)1α(2,2)

1β(2,3) 1
100Fig. 1: Waveforms are case of six cells (M = 2, N =3). Step size is 0.01. k = l = 1.06, m = 1.47.
β(1,1)1:αc(1,2)

c(1,3)

c(1,N):β:βc(2,1)

11New systemj
c(1,1)

α(1,1)

c(2,1):γc(2,2)

c(3,1)

c(3,N)

c(2,3)

c(2,N)

c(3,2)c(3,3)

γ(1,2) 1:γβ(1,2)1c(3,N)

ii
c(i,1)c(i,2)

c(M,1)

c(i,j)

c(M,2)

c(i,1)

c(i,N)

c(M,j)c(i,2)

c(M,1)

c(M,N)

c(i,j)

c(M,2)

α(2,1) 1

c(i,N)

c(M,j)

c(M,N)

α(2,2) 1α(2,3) 1

Table 1: Structure of CNN using three kinds of cloning
templates.
Aα = lAγ = −mk1.24kl−ml1.0lAα = nAγ = −ml−moo1.2400001.0ll

k , Aβ = k

mFig. 2: Waveforms are case of Cell(1, 1), (1, 2), (1, 3),(2, 1), (2, 2) and (2, 3) in one hundred cells (M = 10,N = 10). Step size is 0.05. k = 1.20, l = 1.36, m = 5.5,n = 0.0, o = 2.2.

m ,k1.1m20kln , Aβ = k
001.1mm4. Conclusionsk ,In this study, Cellular Neural Networks using three kindsof cloning templates were investigated. And new system
which cell layout method is changed is proposed. Phenomena of previous system and new system are compared. Asresults, new system can be controlled between cells by parameters. For the future works, phenomena of previous system and new system are investigate in detail.

−m

where k, l, m, n and o show the coupling strengths between40