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

For citation:

Shabunin A. V., Astahov V. V. Phase multistability in an array of period-doubling self­sustained oscillators. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 6, pp. 99-118. DOI: 10.18500/0869-6632-2009-17-6-99-118

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text:
(downloads: 74)
Article type: 

Phase multistability in an array of period-doubling self­sustained oscillators

Shabunin Aleksej Vladimirovich, Saratov State University
Astahov Vladimir Vladimirovich, Yuri Gagarin State Technical University of Saratov

Regularities of multistability developments are considered in an array of identical self-sustained oscillators with transition to chaos through period-doubling bifurcations. The used model is chain of diffusivelly coupled Rossler oscillators. The number of coexisting regimes are determined through the cascade of the bifurcations. It is shown that regularities of incresing of attractors are defined be transformation of the phase spectrum duing transition to chaos.

  1. Astakhov VV, Bezruchko BP, Gulyaev YuV, Seleznev YP. Multistable States Of Dissipatively-Connected Feigenbaum System. Pisma v Zhurnal Tekhnicheskoi Fiziki, 1989;15(3):60–65.
  2. Astakhov VV, Bezruchko BP, Pudovochkin OB, Seleznev EP. Phase multi-stability and establishment of oscillations in nonlinear systems with period doubling. Journal of Communications Technology and Electronics. 1993;38(2):291–295.
  3. Dvornikov AA, Utkin GM, Chukov AM. On the mutual synchronization of the chain of resistively connected auto-generators. Radiophysics and Quantum Electronics. 1984;27(11):1388–1394.
  4. Ermentrout GB. The behavior of rings of coupled oscillators. J Math Biol. 1985;23(1):55--74. DOI: 10.1007/BF00276558.
  5. Ermentrout GB. Stable periodic solutions to discrete and continuum arrays of weakly coupled nonlinear oscillators. SIAM J. of Appl. Math. 1992;52(6):1664–1687. DOI: 10.1137/0152096.
  6. Shabunin AV, Akopov AA, Astakhov VV, Vadivasova TE. Izvestija VUZ, Applied Nonlinear Dynamics. 2005;13(4):37–54 (in Russian).
  7. Astakhov VV, Bezruchko BP, Erastova EN, Seleznev YP. Types of oscillations and their evolution in dissipatively-related feigenbaum systems. Zhurnal Tekhnicheskoi Fiziki. 1990;60(10):19–26.
  8. Astakhov VV, Bezruchko BP, Ponomarenko VI, Seleznev EP. Multi-stability in the system of radio-technical generators with capacitive communication Soviet Journal of Communications Technology and Electronics. 1991;36(11):2167–2170.
  9. Astakhov VV, Bezruchko BP, Ponomarenko VI. Formation of multi-stability, classification of isomers and their evolution in related Feigenbaum systems. Radiophysics and Quantum Electronics. 1991;34(1):35–39.
  10. Anishchenko VS, Astakhov VV, Vadivasova TE, Sosnovtseva OV, Wu CW, Chua L. Dynamics of two coupled Chua’s curcuits. Int. J. of Bifurcation and Chaos. 1995;5(6):1677–1699.
  11. Bezruchko BP, Prokhorov MD, Seleznev EP. Oscillation types, multistability, and basins of attractors in symetrically coupled period-doubling systems. Chaos, Solitons anf Fractals. 2003;15(4):695–711. DOI: 10.1016/S0960-0779(02)00171-6.
  12. Astakhov VV, Shabunin AV, Anishchenko VS. Spectral patterns in the formation of multi-stability in connected generators with doubling of the period. Soviet Journal of Communications Technology and Electronics. 1997;42(8):974.
  13. Matias MA, Perez-Munuzuri V, Marino IP, Lorenzo MN, Perez-Villa V. Size instabilities in ring of chaotic synchronized systems. Europhys. Lett. 1997;37(6):379–384. DOI: 10.1209/EPL/I1997-00159-8.
  14. Matias MA, Guemez J, Perez-Munuzuri V, Marino IP, Lorenzo MN, Perez-Villar V. Observation of a fast rotating wave in rings of coupled chaotic oscillators. Phys. Rev. Lett. 1997;78:219–222.
  15. Marino IP, Perez-Munuzuri V, Perez-Villar V, Sanchez E, Matias MA. Interaction of chaotic rotating waves in coupled rings of chaotic cells. Physica D. 2000;128(2-4):224–235. DOI: 10.1016/s0167-2789(98)00303-0.
  16. Shabunin A, Astakhov V, Anishchenko V. Developing chaos on base of traveling waves in a chain of coupled oscillators with period-doubling. Synchronization and hierarchy of multistability formation. Int. J. of Bifurcation and Chaos. 2002;12(8):1895–1907. DOI: 10.1142/S021812740200556X.
  17. Rossler OE. An equation for continuous chaos. Phys. Lett. A. 1976;57(5):397–398. DOI: 10.1016/0375-9601(76)90101-8.
  18. Blechman II. Synchronization in nature and technology. Moscow: Nauka; 1981. 351 p. (In Russian).
  19. Gurtovnik AS, Neymark YuI. Synchronisms in the system of cyclically weakly coupled oscillators. Dynamic systems: Inter-university collection of scientific works. Nizhny Novgorod: UNN Press; 1991. P. 84.
Short text (in English):
(downloads: 30)