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Modeling nonlinear waves and PDEs via cellular neural networks

Modeling nonlinear waves and PDEs via cellular neural networks Ann. Univ. Ferrara - Sez. VII - Sc. Mat. Suppl. Vol. XLV, 311-326 (1999) Modeling Nonlinear Waves and PDEs via Cellular Neural Networks. ANGELA SLAVOVA (*) To the memory of Lamberto Cattabriga 1. - Introduction. Cellular Neural Networks (CNNs) are nonlinear, continuous computing array structures well suited for nonlinear signal processing. Since its inven- tion in 1988 [2, 3], the investigation of CNNs has envolved to cover a very broad class of problems and frameworks. Many researchers have made signifi- cant contributions to the study of CNN phenomena using different mathemat- ical tools. DEFINITION 1. The CNN is a i) 2-, 3-, or n-dimensional array of ii) mainly identical dynamical systems, called cells, which satisfies two properties: iii) most interactions are local within a finite ,radius r, and iv) all state variables are continuous valued signals. Let us consider a two-dimensional grid with 3 � 3 neighborhood system as it is shown on fig. 1. The squares are the circuit units-cells, and the links between the cells indicate that there are interactions between linked cells. One of the key features of a CNN is that the individual cells are nonlinear dynamical systems, but that the coupling between them is http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ANNALI DELL UNIVERSITA DI FERRARA Springer Journals

Modeling nonlinear waves and PDEs via cellular neural networks

Slavova, Angela
ANNALI DELL UNIVERSITA DI FERRARA , Volume 45 (1) – Jan 1, 1999
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References (12)

Publisher
Springer Journals
Copyright
Copyright © Università degli Studi di Ferrara 1999
ISSN
0430-3202
eISSN
1827-1510
DOI
10.1007/bf02826102
Publisher site
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Abstract

Ann. Univ. Ferrara - Sez. VII - Sc. Mat. Suppl. Vol. XLV, 311-326 (1999) Modeling Nonlinear Waves and PDEs via Cellular Neural Networks. ANGELA SLAVOVA (*) To the memory of Lamberto Cattabriga 1. - Introduction. Cellular Neural Networks (CNNs) are nonlinear, continuous computing array structures well suited for nonlinear signal processing. Since its inven- tion in 1988 [2, 3], the investigation of CNNs has envolved to cover a very broad class of problems and frameworks. Many researchers have made signifi- cant contributions to the study of CNN phenomena using different mathemat- ical tools. DEFINITION 1. The CNN is a i) 2-, 3-, or n-dimensional array of ii) mainly identical dynamical systems, called cells, which satisfies two properties: iii) most interactions are local within a finite ,radius r, and iv) all state variables are continuous valued signals. Let us consider a two-dimensional grid with 3 � 3 neighborhood system as it is shown on fig. 1. The squares are the circuit units-cells, and the links between the cells indicate that there are interactions between linked cells. One of the key features of a CNN is that the individual cells are nonlinear dynamical systems, but that the coupling between them is

Journal

ANNALI DELL UNIVERSITA DI FERRARA – Springer Journals

Published: Jan 1, 1999

Keywords: Periodic Solution; Equilibrium Point; Nonlinear Wave; Spiral Wave; Cellular Neural Network

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