ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Kanakov O. I., Shalfeev V. D. Formation of stationary patterns in lattices of bistable elements with two types of nonlinearity. Izvestiya VUZ. Applied Nonlinear Dynamics, 2005, vol. 13, iss. 3, pp. 77-89. DOI: 10.18500/0869-6632-2005-13-3-77-89

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 128)
Article type: 

Formation of stationary patterns in lattices of bistable elements with two types of nonlinearity

Kanakov Oleg Igorevich, Lobachevsky State University of Nizhny Novgorod
Shalfeev Vladimir Dmitrievich, Lobachevsky State University of Nizhny Novgorod

Laws of pattern formation in lattices of nonlinear-coupled first-order bistable elements with two types of the element nonlinearity are studied and compared. The results are interpreted in terms of the application to edges detection in images. It is shown by the examples considered, that the replacement of the element nonlinearity does not influence significantly the image processing system functionality under certain conditions.

Key words: 
  1. Chua LO, Yang L. Cellular neural networks: Theory. IEEE Trans. Circuits Syst. 1988;35(10):1257–1272. DOI: 10.1109/31.7600.
  2. Chua LO, Yang L. Cellular neural networks: Applications. IEEE Trans. Circuits Syst. 1988;35(10):1273–1290. DOI: 10.1109/31.7601.
  3. Nekorkin VI, Makarov VA, Kazantsev VB, Velarde MG. Spatial disorder and pattern formation in lattices of coupled bistable elements. Physica D. 1997;100(3–4):330–342. DOI: 10.1016/S0167-2789(96)00202-3.
  4. Yakhno VG. Self-organization processes in distributed neuron-like systems. Examples of possible applications. In: Neuroinformatics 2001. Lectures on Neuroinformatics. Moscow: MEPHI; 2001. P. 103–141 (in Russian).
  5. Chua L, Roska T. Cellular Neural Networks and Visual Computing – Foundations and Application. Cambridge University Press; 2002. 410 p. DOI: 10.1017/CBO9780511754494.
  6. Zou F, Nossek A. Bifurcation and chaos in cellular neural networks. IEEE Trans. Circuits Syst. 1993;40(3):166–173. DOI: 10.1109/81.222797.
  7. Zou F, Schwarz S, Nossek JA. Cellular neural networks design using a learning algorithm. In: IEEE International Workshop on Cellular Neural Networks and their Applications CNNA-90. 16-19 Dec. 1990, Budapest, Hungary. New York: IEEE; 1990. P. 73–81. DOI: 10.1109/CNNA.1990.207509.
  8. Kanakov OI, Shalfeev VD. Application of an array of bistable elements with non-identical characteristics to image processing problems. In: Yakimov AV, editor. Proceedings of the VI Scientific Conference on Radiophysics Dedicated to the 100th Anniversary of the Birth of M.T. Grekhova May 7, 2002. Nizhny Novgorod; 2002. P. 116 (in Russian).
  9. Kanakov OI, Shalfeev VD. The influence of the type of nonlinearity of the basic element on pattern formation in a homogeneous CNN. In: Proceedings of the International Symposium Topical Problems of Nonlinear Wave Physics (NWP-2003). Nizhny Novgorod: Institute of Applied Physics RAS; 2003. P. 40–41.
Short text (in English):
(downloads: 62)