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Proceedings Paper

Pattern formation in active oscillatory media and its relation to associative memory networks
Author(s): Margarita Kuzmina; Eduard A. Manykin; Irina I. Surina
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Paper Abstract

We continue to study the arrays of nonlinear coupled oscillators. The networks of associative memory based on limit-cycle oscillators connected via complex-valued Hermnian matrices were previously designed. Another class of networks consisting of locally connected nonlinear oscillators, closely related to so-called cellular neural networks, is the subject of study in the present paper. Within spatially continual limitations, these oscillatory networks can be considered as oscillatory media governed by the system of reaction-diffusion equations. Formation of spatio-temporal dissipative structures (wave trains, standing waves, targets and shock structures, spiral waves, stripe patterns, cluster states) in various nonlinear active media is widely used for modeling of complicated nonlinear phenomena in physics, chemistry, biology, neurophysiology. Here the results of analytical study of 1D oscillatory media corresponding to closed and unclosed chains of limit-cycle oscillators are presented. Conditions of existence of some spatio-temporal regimes inherent to nonlinear active media (diffusion instability caused by coupling, formation of wave trains and standing waves) have been clarified.

Paper Details

Date Published: 28 January 1999
PDF: 10 pages
Proc. SPIE 3733, ICONO '98: Nonlinear Optical Phenomena and Coherent Optics in Information Technologies, (28 January 1999); doi: 10.1117/12.340085
Show Author Affiliations
Margarita Kuzmina, Keldysh Institute of Applied Mathematics (Russia)
Eduard A. Manykin, State Scientific Ctr. Kurchatov Institute (Russia)
Irina I. Surina, State Scientific Ctr. Kurchatov Institute (Russia)

Published in SPIE Proceedings Vol. 3733:
ICONO '98: Nonlinear Optical Phenomena and Coherent Optics in Information Technologies
Sergei S. Chesnokov; Valerii P. Kandidov; Nikolai I. Koroteev, Editor(s)

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