2015 Taiwan and Japan Conference on Circuits and Systems
Shikoku University Plaza, Tokushima, Japan. August 19-21, 2015

Oscillation Phenomena in CNN
with Multi-Cloning Templates
Mana Tanaka† , Yasuteru Hosokawa‡ , Yoko Uwate† and Yoshifumi Nishio††Dept. Electrical and Electronic Eng.,
Tokushima University
Email: mana.8sk@gmail.com, uwate, nishio @ee.tokushima-u.ac.jp‡Dept. Media and Information Syst.,
Shikoku University
Email:hosokawa@keiei.shikoku-u.ac.jp
S UMMARY
There are many studies of coupled chaotic systems. In these systems, various kinds of phenomena are observed. Some ofthese phenomena correspond to natural phenomena. Namely, it is important to investigate coupled chaotic systems. Cellular
Neural Networks ( CNN ) was proposed by Chua and Yang [1][2] in 1988. It is mutual coupling neural networks. Theseare easy to make an integrated circuit and these are parallel processing system. Therefore, many researchers investigate aboutCNN. As one of these studies, CNN using two kinds of cloning templates [3] has been investigated. Mainly, this system ascoupled oscillatory system was investigated. Normally, oscillatory phenomena could not be observed in typical CNN. ThisCNN can be observed oscillatory phenomena. However, chaotic phenomena could not be observed. On the other hand, threecells of CNN generates chaos is reported [4]. Three cells are set different cloning templates. A double scroll type attractor isobserved.
In our previous study, CNN using three kinds of cloning templates was proposed [5]-[7]. Cloning templates are set as
symmetrical templates and corresponding to cloning templates of three cell CNN. This system is a novel coupled chaoticsystem. Three kinds of cells are placed at uniformly in this system. This system has characteristic that elements of oscillating
are shared. The cases of three cells, six cells, nine cells and so on were investigated. Characteristic phenomena are observedin six cells, nine cells, twenty cells and eighteen cells. On the other hand, various phenomena are observed in twenty-fourcells and thirty-six cells. Namely, observed phenomena are influenced by the number of cells. However, relationship between
differences of observed phenomena and the number of cells could not be revealed.
In this study, relationship between differences of observed phenomena and the number of cells is investigated. And classification of oscillatory phenomena are proposed. In any cell, tracing a neighbor cell in turn to one direction reaches the originalcell. Namely, coupled cells are looped. The number of cells is defined as M × N in this system. In the case of N = 3 and M
is multiples of 2, the number of loops is M + 2. On the other hand, In the case of M is multiples of 3, the number of loops
is M + 6. By innovating a counting method of the number of cells, two kinds of observed phenomena can be distinguished.
The case of changing parameters, detailed analysis of two kinds of observed phenomena and so on are our future works.
R EFERENCES[1] L. O. Chua and L. Yang, “Cellular Neural Networks: Theory,” IEEE Trans. Circuits Syst., vol. 35, no. 10, pp. 1257–1272, 1988.
[2] L. O. Chua and L. Yang, “Cellular Neural Networks: Applications,” IEEE Trans. Circuits Syst., vol. 35, no. 10, pp. 1273–1290, 1988.
[3] J. Fujii, Y. Hosokawa and Y. Nishio, “Wave Phenomena in Cellular Neural Networks Using Two Kinds of Template Sets,” Proc. of NOLTA’07, pp. 23–26,2007.
[4] F. Zou, and J. A. Nossek, “Bifurcation and chaos in cellular neural networks,” IEEE Trans. Circuits Syst. I, vol. 40, no. 3, pp. 166–173, 1993.
[5] M. Tanaka, Y. Hosokawa and Y. Nishio, “Chaotic Phenomena in Cellular Neural Networks Using Three Kinds of Cloning Templates,” Proc. of NCN’13,pp. 30–33, 2013.
[6] M. Tanaka, Y. Hosokawa and Y. Nishio, “Relationship between a Number of Cells and Phenomena in Cellular Neural Networks Using Three Kinds ofCloning Templates,” RISP Proc. NCSP’14, pp533–536, 2014.
[7] M. Tanaka, Y. Hosokawa and Y. Nishio, “Immobilization of Oscillation Groups in CNN Using Three Kinds of Cloning Templates,” Proc. of NCN’14,
pp. 98–101, 2014.

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