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.E80-A   No.1   pp.214-222
Publication Date: 1997/01/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Neural Networks
Keyword: 
coupled oscillators,  hexagonal circuit,  lattice circuit,  cellular neural network,  

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Summary: 
When N oscillators are coupled by one resistor, we can see N-phase 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, 2-phase oscillation and get much more phase states. In this study, the two types of coupled oscillators networks with third and fifth-power nonlinear characteristics are proposed. One network has two-dimensional hexagonal structure and the other has two-dimensional 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 third-power nonlinear characteristics, we can see the phase patterns based on 3-phase oscillation in the hexagonal circuit, and based on anti-phase oscillation in lattice circuit. In the system with fifth-power nonlinear characteristics, we can see the phase patterns based on 3-phase and anti-phase oscillation in both hexagonal and lattice circuits. In particular, in these networks, we can see not only the synchronization based on 3-phase and anti-phase oscillation but the synchronization which is not based on 3-phase and anti-phase oscillation.