DETECTION OF UNSTABLE PERIODICAL SPATIO-TEMPORAL STATES OF SPATIAL EXTENDED CHAOTIC SYSTEMS DYNAMICS
Cite this article as:
Koronovskii A. A., Hramov A. E. DETECTION OF UNSTABLE PERIODICAL SPATIO-TEMPORAL STATES OF SPATIAL EXTENDED CHAOTIC SYSTEMS DYNAMICS. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 4, pp. 26-33. DOI: https://doi.org/10.18500/0869-6632-2007-15-4-26-33
The method of detection of the unstable periodic spatio-temporal states of spatial extended chaotic systems dynamics is proposed. The application of this method is illustrated by the consideration of the fluid model of Pierce diode which is one of the base system of plasma physics and of microwave electronics.
1. Cvitanovic P. ́ Periodic orbits as the skeleton of classical and quantum chaos // Physica D. 1991. Vol. 51. P. 138.
2. Barreto E., Hunt B.R., Grebogi C., Yorke J.A. From high dimension chaos to stable periodic orbits: The structure of parameter space // Phys. Rev. Lett. 1997. Vol. 78(24). P. 4561.
3. Carroll T.L. Approximating chaotic time series through unstable periodic orbits // Phys. Rev. E. 1999. Vol. 59 (2). P. 1615.
4. Pikovsky A.S., Grassberger P. Symmetry breaking bifurcation for coupled chaotic attractors // J. Phys. A. 1991. Vol. 24. P. 4587.
5. Pikovsky A.S., Zaks M., Rosenblum M.G., Osipov G.V., Kurths J. Phase synchronization of chaotic oscillators in terms of periodic orbits // Chaos. 1997. Vol. 7 (4). P. 680.
6. Hramov A.E., Koronovskii A.A., Kurovskaya M.K., Moskalenko O.I. Synchronization of spectral components and its regularities in chaotic dynamical systems // Phys. Rev. E. 2005. Vol. 71 (5). P. 056204.
7. Pyragas K. Continuous control of chaos, by self-controlling feedback // Phys. Lett. A. 1992. Vol. 170. P. 421.
8. Lathrop D.P., Kostelich E.J. Characterization of an experimental strange attractor by periodic orbits // Phys. Rev. A. 1989. Vol. 40 (7). P. 4028.
9. Schmelcher P., Diakonos F.K. Detecting unstable periodic orbits of chaotic dynamical systems // Phys. Rev. Lett. 1997. Vol. 79 (25). P. 4734.
10. Pingel D., Schmelcher P., Diakonos F.K. Detecting unstable periodic orbits in chaotic continuous-time dynamical systems // Phys. Rev. E. 2001. Vol. 64 (2). P. 026214.
11. Короновский А.А., Ремпен И.С., Храмов А.Е. Исследование неустойчивых периодических пространственно-временных состояний в распределенной автоколебательной системе со cверхкритическим током // Изв. РАН, сер. физич. 2003. Т. 67 (12). С. 1705.
12. Ремпен И.С., Храмов А.Е. Стабилизация нестойчивых периодических состояний хаотической динамики в диоде Пирса // Изв. РАН, сер. физич. 2004. Т. 68 (12). С. 1789.
13. Franceschini G., Bose S., Scholl E. ̈ Control of chaotic spatiotemporal spiking by time-delay autosynchronization // Phys. Rev. E. 1999. Vol. 60 (5). P. 5426.
14. Hramov A.E., Koronovskii A.A., Rempen I.S. Controlling chaos in spatially extended beam-plasma system by the continuous delayed feedback // Chaos. Vol. 16 (1) P. 013123.
15. Friedel H., Grauer R., Spatschek H.K. Contolling chaotic states of a Pierce diode // Physics of plasmas. 1998. Vol. 5 (9). P. 3187.
16. Анфиногентов В.Г. Хаотические колебания в электронном потоке с виртуальным катодом // Изв. вузов. Прикладная нелинейная динамика. 1994. Т. 2, No 5. С. 69.
17. Трубецков Д.И., Храмов А.Е. Лекции по сверхвысокочастотной электронике для физиков. Т. 1. М.: Физматлит, 2003.
18. Godfrey B.B. Oscillatory nonlinear electron flow in Pierce diode // Phys. Fluids. 1987. Vol. 30. P. 1553.
19. Анфиногентов В.Г., Трубецков Д.И. Хаотические колебания в гидродинамической модели диода Пирса // Радиотехника и электроника. 1992. Т. 37. С. 2251.
20. Matsumoto H., Yokoyama H., Summers D. Computer simulations of the chaotic dynamics of the Pierce beam–plasma system // Phys. Plasmas. 1996. Vol. 3 (1). P. 177.
21. Hramov A.E., Rempen I.S. Investigation of the complex dynamics and regime control in Pierce diode with the delay feedback // Int. J.Electronics. 2004. Vol. 91 (1). P. 1.
22. Pecora L.M., Carroll T.L., Heagy J.F. Statistics for mathematical properties of maps between time series embeddings // Phys. Rev. E. 1995. Vol. 52 (4). P. 3420.
BibTeX
author = {A. A. Koronovskii and A. E. Hramov},
title = {DETECTION OF UNSTABLE PERIODICAL SPATIO-TEMPORAL STATES OF SPATIAL EXTENDED CHAOTIC SYSTEMS DYNAMICS},
year = {2007},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {15},number = {4},
url = {https://old-andjournal.sgu.ru/en/articles/detection-of-unstable-periodical-spatio-temporal-states-of-spatial-extended-chaotic-systems},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2007-15-4-26-33},pages = {26--33},issn = {0869-6632},
keywords = {-},
abstract = {The method of detection of the unstable periodic spatio-temporal states of spatial extended chaotic systems dynamics is proposed. The application of this method is illustrated by the consideration of the fluid model of Pierce diode which is one of the base system of plasma physics and of microwave electronics. }}