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On Coupled Oscillators Networks for Cellular Neural Networks
Seiichiro MORO Yoshifumi NISHIO Shinsaku MORI
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E80A
No.1
pp.214222 Publication Date: 1997/01/25 Online ISSN:
DOI: Print ISSN: 09168508 Type of Manuscript: PAPER Category: Neural Networks Keyword: coupled oscillators, hexagonal circuit, lattice circuit, cellular neural network,
Full Text: PDF>>
Summary:
When N oscillators are coupled by one resistor, we can see Nphase oscillation, because the system tends to minimize the current through the coupling resistor. Moreover, when the hard oscillators are coupled, we can see N, N  1, , 3, 2phase oscillation and get much more phase states. In this study, the two types of coupled oscillators networks with third and fifthpower nonlinear characteristics are proposed. One network has twodimensional hexagonal structure and the other has twodimensional lattice structure. In the hexagonal circuit, adjacent three oscillators are coupled by one coupling resistor. On the other hand, in the lattice circuit, four oscillators are coupled by one coupling resistor. In this paper we confirm the phenomena seen in the proposed networks by circuit experiments and numerical calculations. In the system with thirdpower nonlinear characteristics, we can see the phase patterns based on 3phase oscillation in the hexagonal circuit, and based on antiphase oscillation in lattice circuit. In the system with fifthpower nonlinear characteristics, we can see the phase patterns based on 3phase and antiphase oscillation in both hexagonal and lattice circuits. In particular, in these networks, we can see not only the synchronization based on 3phase and antiphase oscillation but the synchronization which is not based on 3phase and antiphase oscillation.

