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


For citation:

Prokhorov M. D. Oscillation types of dissipatively coupled period doubling systems at strong coupling. Izvestiya VUZ. Applied Nonlinear Dynamics, 1996, vol. 4, iss. 4, pp. 99-107.

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: 0)
Language: 
Russian
Heading: 
Article type: 
Article
UDC: 
530.18

Oscillation types of dissipatively coupled period doubling systems at strong coupling

Autors: 
Prokhorov Mihail Dmitrievich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract: 

Oscillation types of two symmetrically coupled identical systems demonsirating period doubling are considered. For the case of dissipative coupling it is shown that outof-phase oscillation regimes exist not only at weak coupling between subsystems (k ~ 0), but also at very strong coupling (k ~ 1). In the system parameter space the regions of out-of-phase regimes are symmetrical about k=0.5. However, in spite of symmetry the out-of-phase regimes at weak and strong coupling are essentially different.

Key words: 
Reference: 
  1. Kuznetsov SP. Universality and scaling in the behavior of coupled Feigenbaum systems. Radiophys. Quantum Electron. 1985;28(8):681-695. DOI: 10.1007/BF01035195.
  2. Buskirk R, Jeffries С. Observation of chaotic dynamics of coupled nonlinear оscillators. Phys. Rev. А. 1985;31(5):3332-3357. DOI: 10.1103/physreva.31.3332.
  3. Gu Y, Tung M, Yuan JM, Feng DH, Narducci LM. Crises and hysteresis in coupled logistic maps. Phys. Rev. Lett. 1984;52(9):701-704. DOI: 10.1103/PhysRevLett.52.701.
  4. Dmitriev AS, Starkov SO, Shirokov ME. Synchronisation of ensembles of dissipatively related mappings. Preprint № 9 (609) Institute of Radio Engineering and Electronics RAS. М.; 1995. 38 p.
  5. Satoh K, Aihara Т. Numerical study оn а coupled-logistic map аs а simple model for а predator-prey system. J. Phys. Soc. Jpn. 1990;59(4):1184-1198.
  6. Reick C, Mosekilde E. Emergence of quasiperiodicity in symmetrically coupled, identical period-doubling systems. Phys. Rev. Е. 1995;52(2):1418-1435. DOI: 10.1103/PhysRevE.52.1418.
  7. Crutchfield JP, Kaneko K. Phenomenology of spatio-temporal chaos. In: Directions in chaos. Vol. 1. Singapore: World Scientific; 1987. P. 272-353. DOI: 10.1142/9789814415712_0008.
  8. Astakhov VV, Bezruchko BP, Erastova EN, Seleznev VP. Types of oscillations and their evolution in dissipatively related Feigenbaum systems. Tech. Phys. 1990;60(10):19-26.
  9. Bezruchko BP, Seleznev ЕP, Smirnov ЕV. Evolution of attraction basins of attractors of symmetrically connected systems with period doubling. Tech. Phys. Lett. 1995;21(8):12-17.
  10. Bezruchko BP, Prokhorov МD, Seleznev ЕP. Features of the device of the space of parameters of two related non-autonomous non-isochrone oscillators. Tech. Phys. Lett. 1996;22(6):61-66.
Received: 
18.04.1996
Accepted: 
23.09.1996
Published: 
10.12.1996