STABILIZATION OF CHAOS IN THE ROSSLER SYSTEM BY PULSED OR HARMONIC SIGNAL


Cite this article as:

Kuznetsov A. P., Stankevich N. V., Chernyshov N. Y. STABILIZATION OF CHAOS IN THE ROSSLER SYSTEM BY PULSED OR HARMONIC SIGNAL. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 4, pp. 3-16. DOI: https://doi.org/10.18500/0869-6632-2010-18-4-3-16


The stabilization of chaos in the Rossler system by external signal is investigated. Different types of external action are considered: both of pulsed and harmonic signal. There are illustrations: charts of dynamical regimes, phase porters, stroboscopic section of Poincare, spectrum of Lyapunov exponents. Comparative analysis of efficiency of stabilization of band chaos and spiral chaos by different signal is carried out. The dependence of synchronization picture on direction of acting pulses is shown.

DOI: 
10.18500/0869-6632-2010-18-4-3-16
Literature

1. Ott E. Chaos in Dynamical Systems. Cambridge University press, 1993.

2. Анищенко В.С., Вадивасова Т.Е., Астахов В.В. Нелинейная динамика хаотических и стохастических систем. Фундаментальные основы и избранные проблемы. Саратов, 1999. 368 с.

3. Пиковский А., Розенблюм М., Куртс Ю. Синхронизация. Фундаментальное нелинейное явление. М.: Техносфера, 2003. 494 c.

4. Schuster H.G. Handbook of Chaos Control. Wiley-VCH, Weinheim, 1999.

5. Boccaletti S., Grebogi C., Lai Y.C., Mancini H., and Maza D. The control of chaos: theory and applications // Physics Reports – Review Section of Physics Letters. 2000. Vol. 329. P. 103.

6. Gauthier D., Hall G.M., Olivier R.A., Dixon-Tulloch E.G., Wolf P.D., and Bahar S. Progress toward controlling in vivo fibrillating sheep atria using a nonlinear dynamics based closed loop feedback method // CHAOS. 2002. Vol. 12. P. 952.

7. Ott E., Grebogi C. and Yorke J.A. Controlling chaos // Phys. Rev. Lett. 1990. Vol. 64. 1196.

8. Mori H., Kuramoto Y. Dissipative Structures and Chaos. Springer, 1998.

9. Stone E.F. Frequency entrainment of phase coherent attractor // Physics Letters A. 1992. Vol. 163. P. 367.

10. Rossler O.E. An equation for continuous chaos // Physics Letters A. 1976. Vol. 57. P. 397.

11. Rossler O.E. Chaos in abstract kinetics: Two prototypes // Bulletin of Mathematical Biology. 1977. Vol. 39. P. 275.

12. Кузнецов С.П. Динамический хаос. М.: Физматлит, 2001. 296 с.

13. Kuznetsov S.P., Sataev I.R. Universality and scaling for the breakup of phase synchronization at the onset of chaos in a periodically driven Roessler oscillator // Phys.Rev. E. 2001. Vol. 64. 046214.

14. Кузнецов А.П., Станкевич Н.В., Тюрюкина Л.В. Особенности синхронзации импульсами в системе с трехмерным фазовым пространством на примере системы Ресслера // Изв. вузов. ПНД. 2006. Т. 14, No 6. С. 43.

15. Кузнецов А.П., Станкевич Н.В., Тюрюкина Л.В. Стабилизация внешними импульсами системы Ресслера в режиме «убегающей траектории» // Письма в ЖТФ. 2008. Т. 34, вып. 14. С. 68.

16. Ding E.J. Structure of parameter space for a prototype nonlinear oscillator // Phys. Rev. 1987. Vol. A36, No 3. P. 1488.

17. Ding E.J. Structure of the parameter space for the van der Pol oscillator // Physica Scripta. 1988. Vol. 38. P. 9.

18. Glass L., Sun J. Periodic forcing of a limit-cycle oscillator: Fixed points, Arnold tongues, and the global organization of bifurcations // Phys. Rev. 1994. Vol. 50, No 6. P. 5077.

19. Carcasses J., Mira C., Bosch M., Simo C., Tatjer J.C. «Crossroad area – spring area» transition (I) Parameter plane representation // Int. J. Bif. and Chaos. 1991. Vol. 1. No 1. P. 183.

20. Carcasses J., Mira C., Bosch M., Simo C., Tatjer J.C. «Crossroad area – spring area» transition (II) Foliated parametric representation // Int. J. Bif. and Chaos. 1991. Vol. 1. No 2. P. 339.

Status: 
одобрено к публикации
Short Text (PDF): 
Full Text (PDF): 

BibTeX

@article{Кузнецов-IzvVUZ_AND-18-4-3,
author = {A. P. Kuznetsov and Nataliya Vladimirovna Stankevich and N. Yu. Chernyshov},
title = {STABILIZATION OF CHAOS IN THE ROSSLER SYSTEM BY PULSED OR HARMONIC SIGNAL},
year = {2010},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {18},number = {4},
url = {https://old-andjournal.sgu.ru/en/articles/stabilization-of-chaos-in-the-rossler-system-by-pulsed-or-harmonic-signal},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2010-18-4-3-16},pages = {3--16},issn = {0869-6632},
keywords = {External action,chaos,stabilization},
abstract = {The stabilization of chaos in the Rossler system by external signal is investigated. Different types of external action are considered: both of pulsed and harmonic signal. There are illustrations: charts of dynamical regimes, phase porters, stroboscopic section of Poincare, spectrum of Lyapunov exponents. Comparative analysis of efficiency of stabilization of band chaos and spiral chaos by different signal is carried out. The dependence of synchronization picture on direction of acting pulses is shown. }}