CONTROLL OF MULTISTABILITY BY MEANS OF BIPHASE RESONANCE FORCE
Cite this article as:
Shabunin А. V., Litvinenko А. N., Astakhov V. V. CONTROLL OF MULTISTABILITY BY MEANS OF BIPHASE RESONANCE FORCE. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 1, pp. 25-39. DOI: https://doi.org/10.18500/0869-6632-2011-19-1-25-39
We propose a new method of control of phase multistability in two coupled selfsustained oscillators. The method is based on the «pulling» of phases of oscillations to the target mode under two external harmonic forces, which influence the first and the second subsystems simultaneosly. Varying the phase shift between the external signals results in control of switching between coexisting oscillating modes. Effectiveness of the method is demonstrated on the example of switching between periodic and chaotic regimes in two Chua’s oscillatotrs.
1. Arecchi F.T., Meucci R., Puccioni G., Tredicce J. Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser // Phys. Rev. Lett. 1982. Vol. 49. P. 1217.
2. Prengel F., Wacker A. Scholl E. Simple model for multistability and domain formation in semiconductor superlattices // Phys. Rev. B. 1994. Vol. 50. P. 1705.
3. Sun N.G., Tsironis G.P. Multistability of conductance in doped semiconductor superlattices // Phys. Rev. B. 1995. Vol. 51. P. 11221.
4. Foss J., Longtin A., Mensour B., Milton J. Multistability and delayed recurrent loops // Phys. Rev. Lett. 1996. Vol. 76. P. 708.
5. Астахов В.В., Безручко Б.П., Гуляев Ю.П., Селезнев Е.П. Мультистабильные состояния в диссипативно связанных фейгенбаумовских системах // Письма в ЖТФ. 1989. Т. 15, No 3. C. 60.
6. Астахов В.В., Безручко Б.П., Ерастова Е.Н., Селезнев Е.П. Формы колебаний и их эволюция в диссипативно связанных фейгенбаумовских системах // Журнал Технической Физики. 1990. Т. 60, No 10. С. 19.
7. Дворников А.А., Уткин Г.М., Чуков А.М. О взаимной синхронизации цепочки резистивно связанных автогенераторов // Известия вузов. Радиофизика. 1984. Т. 27, No 11. С. 1388.
8. Ermentrout G.B. The behaviour of rings of coupled oscillators // J. of Math. Biol. 1985. Vol. 23, No 1. P. 55.
9. Ermentrout G.B. Stable periodic solutions to discrete and continuum arrays of weakly coupled nonlinear oscillators // SIAM J. of Appl. Math. 1992. Vol. 52, No 6. P. 1664.
10. Matias M.A., Guemez J., Perez-Munuzuri V., Marino I.P., Lorenzo M.N., Perez-Villar V. Observation of a fast rotating wave in rings of coupled chaotic oscillators // Phys. Rev. Lett. 1997. Vol. 78, No 2. P. 219.
11. Balanov A.G., Janson N.B., Astakhov V.V., McClintock P.V.E. Role of saddle tori in the mutual synchronization of periodic oscillations // Phys. Rev. E. 2005. Vol. 72. 026214.
12. Астахов В.В., Шабунин А.В., Анищенко В.С. Спектральные закономерности при формировании мультистабильности в связанных генераторах с удвоением периода // Радиотехника и Электроника. 1997. Т. 42, No 8. С. 974.
13. Shabunin A., Feudel U., Astakhov V. Phase multistability and phase synchronization in an array of locally coupled period-doubling oscillators // Phys. Rev. E. 2009. Vol. 80. 026211.
14. Bezruchko B.P., Prokhorov M.D., Seleznev E.P. Oscillation types, multistability, and basins of attractors in symetrically coupled period-doubling systems // Chaos, Solitons anf Fractals. 2003. Vol. 15. P. 695.
15. Lai Y.-C. Driving trajectories to a desirable attractor by using small control // Phys. Lett. A. 1996. Vol. 221. P. 375.
16. Macau E.E.N., Grebogi C. Driving trajectories in complex systems // Phys. Rev. E. 1999. Vol. 59. P. 4062.
17. Pisarchik A.N., Goswami B.K. Annihilation of one of the coexisting attractors in a bistable system // Phys. Rev. Lett. 2000. Vol. 84. P. 1423.
18. Егоров Е.Н., Короновский А.А. К вопросу об управлении динамическими режимами в системе, демонстрирующей мультистабильность // Письма в ЖТФ. 2004. Т. 30, вып. 5. Стр. 30.
19. Goswami B.K., Euzzor S., Naimee K.A., Geltrude A., Meucci R., Arecchi F.T. Control of stochastic multistable systems: Experiment demonstration // Phys. Rev. E. 2009. Vol. 80. 016211.
20. Goswami B.K. Control of multistate hopping intermittency // Phys. Rev. E. 2008. Vol. 78. 066208.
21. Астахов В.В., Щербаков М.Г., Коблянский С.А., Шабунин А.В. Синхронизация пространственно-периодических режимов цепочки генераторов с фазовой мультистабильностью // Изв. вузов. Прикладная нелинейная динамика. 2008. Т. 16, No 4. С. 65.
22. Komuro M., Tokunaga R., Matsumoto T., Chua L.O., Hotta A. Global bifurcation analysis of the double-scroll circuit // Int. J. Bifurcation and Chaos. 1991. Vol. 1, No 1. P. 139.
23. Khibnik A.I., Roose D.,Chua L. // Chua’s сircuit: A paradigm for chaos. Singapour: World Scientific, 1993. P. 145.
24. Anishchenko V.S., Astakhov V.V., Vadivasova T.E., Sosnovtseva O.V., Wu C.W., Chua L. Dynamics of two coupled Chua’s curcuits // Int. J. of Bifurcation and Chaos. 1995. Vol. 5, No 6. P. 1677.
25. Блехман И.И. Синхронизация в природе и технике. М.: Наука, 1981.
BibTeX
author = {А. V. Shabunin and А. N. Litvinenko and V. V. Astakhov},
title = {CONTROLL OF MULTISTABILITY BY MEANS OF BIPHASE RESONANCE FORCE},
year = {2011},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {19},number = {1},
url = {https://old-andjournal.sgu.ru/en/articles/controll-of-multistability-by-means-of-biphase-resonance-force},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2011-19-1-25-39},pages = {25--39},issn = {0869-6632},
keywords = {Phase multistability,synchronization,control of multistability.},
abstract = {We propose a new method of control of phase multistability in two coupled selfsustained oscillators. The method is based on the «pulling» of phases of oscillations to the target mode under two external harmonic forces, which influence the first and the second subsystems simultaneosly. Varying the phase shift between the external signals results in control of switching between coexisting oscillating modes. Effectiveness of the method is demonstrated on the example of switching between periodic and chaotic regimes in two Chua’s oscillatotrs. }}