Relationship between Oscillatory Phenomena andthe Number of Cells in Two-Template CNN
Junji Fujii

Yasuteru Hosokawa

Yoshifumi Nishio

Dept. Information Science,Shikoku University
i1739082@keiei.shikoku-u.ac.jp

Dept. Information Science,
Shikoku University
hosokawa@keiei.shikoku-u.ac.jp

Dept. Electrical and Electronic Eng.,
Tokushima University
nishio@ee.tokushima-u.ac.jp

I. SUMMARY
We have proposed a two template CNN as shown in following equation.
1: The case that i + j is an even number.
∑∑dxij= −xij + Iα +Aα (i, j; k, l)ykl +Bα (i, j; k, l)ukl
dtc(k,l)(1)c(k,l)

2: The case that i + j is an odd number.
∑∑dxij= −xij + Iβ +Aβ (i, j; k, l)ykl +Bβ (i, j; k, l)ukl
dtc(k,l)(2)c(k,l)

A{αβ} (i, j; k, l)ykl , B{αβ} (i, j; k, l)ukl and I{αβ} are called as the feedback coefﬁcient, the control coefﬁcient and the bias
current, respectively. The output equation of the cell is given as follows:yij = f (xij ).

(3)f (x) = 0.5(|x + 1| − |x − 1|).

(4)

where,The variables u and y are the input and output variables of the cell, respectively.
This system was proposed in order to investigate a new class of coupled oscillatory systems. The system consists of using
two kinds of oscillatory factor. Additionally, the two kinds of oscillatory factors are arranged in a checkered pattern. Factorsof oscillation is shared each others. Namely, two kinds of oscillatory factors are needed for a simple oscillation. It is not soeasy to implement this structure by using oscillatory circuit. Complex oscillatory phenomena are observed in the case thatthe number of cells are set as 49×49. However, in the case that the number of cells set as 3×3, only a simple synchronizedpattern is observed.
In this study, the relationship between oscillatory phenomena and the number of cells is investigated. Investigated numbersof cells are 3×3, 5×5, 7×7, . . . , 49×49. Namely, the cases that the numbers of rows and columns is set as odd numbers areinvestigated. In the case of even numbers, the system becomes an asymmetry and many complex phenomena are observed.
For this reasons, we investigate the case of odd numbers only. By computer simulations, we could conﬁrm that oscillatory
phenomena were divided as two patterns. The two patterns are the case of oscillating and the case of oscillating boundary
cells. Additionally, parameter regions of oscillators are investigated.
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