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


For citation:

Ivanova A. S., Kuznetsov S. P. Wave оf clusterization in а chain оf coupled cells еаch оf which is composed of a set of globally coupled elements. Izvestiya VUZ. Applied Nonlinear Dynamics, 2003, vol. 11, iss. 4, pp. 80-88. DOI: 10.18500/0869-6632-2003-11-4-80-88

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
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Language: 
Russian
Article type: 
Article
UDC: 
517.9

Wave оf clusterization in а chain оf coupled cells еаch оf which is composed of a set of globally coupled elements

Autors: 
Ivanova Anna Sergeevna, Saratov State University
Kuznetsov Sergey Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract: 

We study chains оf cells each оf which is а set оf globally coupled elements. Under definite conditions, we observe numerically propagation of a wave of clusterization: an image presented originally in one cell is formed gradually, in а course оf evolution in time, also in other cells of the chain.

Key words: 
Acknowledgments: 
The work was supported by the Ministry of Industry and Science under the agreement with the IPF RAS and the RFBR grant No. 03-02-16074.
Reference: 
  1. Vedenov AA, editor. Results of Science and Technology. Ser. “Physical and Mathematical Models of Neural Networks”. Vol. 1-5. Moscow: VINITI; 1990-1992 (in Russian).
  2. Kogan AB. From Neurophysiology to Neurocybernetics. Moscow: Nauka; 1975. 150 p. (in Russian).
  3. Wasserman PD. Neural Computing: Theory and Practice. Coriolis Group; 1989. 230 p.
  4. Hopfield JJ. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA. 1982;79(8):2554-2558. DOI: 10.1073/pnas.79.8.2554
  5. Kaneko K. Clustering, coding, switching, hierarchical ordering, and control in network оf chaotic elements. Physica D. 1990;41(2):137-172. DOI: 10.1016/0167-2789(90)90119-A.
  6. Glendenning P. The stability boundary of synchronized states in globally coupled dynamical systems. Phys. Lett. А. 1999;259(2):129-134. DOI: 10.1016/S0375-9601(99)00417-X.
  7. Popovich O, Pikovsky А, Maistrenko Y. Cluster-splitting bifurcation in а system оf coupled maps. Physica D. 2002;168-169:106-125. DOI: 10.1016/S0167-2789(02)00499-2.
  8. Balmforth NJ, Provenzale А, Sassi К. A hierarchy оf coupled maps. Chaos. 2002;12(3):719-731. DOI: 10.1063/1.1502929.
  9. Rosenblatt F. Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms. Spartan Books; 1962. 616 p.
  10. Kuznetsov SP. Universality and scaling in the behavior of coupled Feigenbaum systems. Radiophysics and Quantum Electronics. 1985;28(8):681–695.
  11. Kook H, Ling FH, Schmidt С. Universal behavior оf coupled nonlinear systems. Phys. Rev. А. 1991;43(6):2700-2708. DOI: 10.1103/PhysRevA.43.2700.
  12. Kim S-Y, Kook H. Renormalization analysis оf two coupled maps. Phys. Lett. А. 1993;178(3-4):258-264. DOI: 10.1016/0375-9601(93)91099-Q.
  13. Feigenbaum MJ. Quantitative universality for а class оf nonlinear transformations. J. Stat. Phys. 1978;19(1):25-52. DOI: 10.1007/BF01020332.
  14. Kuznetsov SP. Universality and scaling in two-dimensional coupled map lattices. Chaos, Solitons and Fractals. 1992;2(3):281-301. DOI: 10.1016/0960-0779(92)90037-N.
Received: 
28.02.2003
Accepted: 
02.06.2003
Available online: 
30.11.2023
Published: 
31.12.2003