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

For citation:

Kazantsev V. B., Nekorkin V. I. Information transport in active electronic fibers. Part I. Solitary waves. Izvestiya VUZ. Applied Nonlinear Dynamics, 1998, vol. 6, iss. 3, pp. 49-66. DOI: 10.18500/0869-6632-1998-6-3-49-66

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Language: 
Russian
Heading: 
Autowaves. Self-organization
Article type: 
Article
UDC: 
621.373.1
DOI: 
10.18500/0869-6632-1998-6-3-49-66

Information transport in active electronic fibers. Part I. Solitary waves

Autors: 
Kazantsev Viktor Borisovich, Institute of Applied Physics of the Russian Academy of Sciences
Nekorkin Vladimir Isaakovich, Institute of Applied Physics of the Russian Academy of Sciences
Abstract: 

We consider the chain of coupled electronic cells as active electronic fiber capable in make the efiective transport of infermation coded in sequences of solitary pulses. The prooblem of the existence of solitary pulses is reduced to the analysis of bounded traectories of some auxiliary ODE system of the fourth order. It is shown that for certain parameter values there realize homo— and hetercclinic orbits of different types including complicated, multi-looped solutions. These orbits define the profiles of pulses, wave fronts ап wave trains sleady translating in the original chain.

Key words: 
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Acknowledgments: 
The work was supported by the RFBR (project 97-02-16550), by grant 96-1596593 for the support of leading scientific schools of the Russian Federation and the Soros Graduate Students Program (grant a97-853).
Reference: 
  1. Haus HA. Waves and Fields in Optoelectronics. New Jersey: Prentice-Hall; 1984. 402 p.
  2. Agrawal GP. Nonlinear Fiber Optics. Boston: Academic Press; 1989. 342 p.
  3. Hasegawa А, Kodama Y. Solitons in Optical Communications. Oxford: Oxford University Press; 1995. 334 p.
  4. Guoxiang Huang, Velarde MG. Head-on collisions оf dark solitons near the zero-dispersion point in optical fibers. Phys. Rev. E. 1996;54(3):3048-3051. DOI: 10.1103/physreve.54.3048.
  5. Scott A. Active and Nonlinear Wave Propagation in Electronics. N.Y.: Wiley; 1970. 326 p.
  6. Vasilyev VA, Romanovskii YuM, Yakhno VG. Autowave Processes. M.: Nauka; 1987. 240 p. (in Russian).
  7. Murray JD. Mathematical Biology. Berlin: Springer; 1993. 770 p. DOI: 10.1007/978-3-662-08542-4.
  8. Krinskii VI, Medvedinskii AB, Panfilov AV. Evolution of Autowave Vortices. M.: Znanie; 1986. 48 p. (in Russian).
  9. Longren K, Scott AC, editors. Solitons in Action. N.Y.: Academic Press; 1978. 300 p.
  10. Barone A, Paterno G. Physics and Applications of the Josephson Effect. N.Y.: Wiley; 1982. 529 p.
  11. 1996 Fourth IEEE Iaternational Workshop оn Cellular Neural Networks and their Applications. Proceedings. Sevilla, Spain;1996.
  12. Madan RN, editor. Chua’s Circuit: а Paradigm for Chaos. Singapore: World Scientific; 1993. 1088 p. DOI: 10.1142/1997.
  13. Nekorkin VI, Chua LО. Spatial disorder and wave fronts in а chain оf coupled Chua’s circuits. Int. J. Bifurc. Chaos. 1993;3(5):1281-1291. DOI: 10.1142/S0218127493001021.
  14. Nekorkin VI, Kazantsev VB, Rulkov NF, Velarde MG, Chua LO. Ноmо-chric orbits and solitary waves in а one—dirnensional array оf Chua’s circuits. IEEE Trans. Circ. Syst. 1995;42(10):785-801. DOI: 10.1109/81.473588.
  15. Nekorkin VI, Kazantsev VB, Velarde MG. Travelling waves in a circular array of Chua’s circuits. Int. J. Bifurc. Chaos. 1996;6(3):473-484. DOI: 10.1142/S0218127496000199.
  16. Kazantsev VB, Nekorkin VI, Velarde MG. Pulses, fronts and chaotic wave trains in а one—dimensional Chua’s lattice. Int. J. Bifurc. Chaos. 1997;7(8):1775-1790. DOI: 10.1142/S0218127497001369.
  17. Shilnikov LP. On one new type of bifurcation of multidimensional dynamical systems. Soviet Phys. Doklady. 1969;189(1):59-62.
  18. Shilnikov LP. A contribution to the problem of the structure of an extended neighbourhood of a rough equilibrium state of saddle-focus type. Mathematics of the USSR-Sbornik. 1970;10(1):91-102. DOI: 10.1070/sm1970v010n01abeh001588.
Received: 
09.05.1998
Accepted: 
13.09.1998
Published: 
15.01.1999
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