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


For citation:

Ajdarova J. S., Kuznetsov A. P., Turukina L. V. The comparative analysis of synchronization by a harmonious and pulse force by the example of lorentz system. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 4, pp. 55-67. DOI: 10.18500/0869-6632-2007-15-4-55-67

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: 135)
Language: 
Russian
Heading: 
Article type: 
Article
UDC: 
517.9

The comparative analysis of synchronization by a harmonious and pulse force by the example of lorentz system

Autors: 
Ajdarova Julija Serikovna, Saratov State University
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Turukina L. V., Saratov State University
Abstract: 

The synchronization by external periodic force of Lorenz system is under both numeric and analytical investigation in this paper. Properly studied the changes in synchronization caused by alteration of parameter value, which is responsible for arising of chaotic attractor in autonomous system.  

Key words: 
Reference: 
  1. Neimark YuI, Landa PS. Stochastic and Chaotic Oscillations. Moscow: Nauka; 1987. (in Russian).
  2. Berge P, Pomo I, Vidal C. Order in Chaos. Moscow: Mir; 1991. (in Russian).
  3. Ott E. Chaos in dynamical systems. Cambridge University Press; 1993.
  4. Anishchenko VS. Complex Oscillations in Simple Systems. Moscow: Nauka; 1990. (in Russian).
  5. Winfree AT. The Geometry of Biological Time. Berlin: Springer-Verlag; 1980.
  6. Pikovsky A, Rosenblum M, Kurts Yu. Synchronization: A fundamental nonlinear phenomenon. Moscow: Tehnosphera; 2003. 493 p.
  7. Mosekilde E, Maistrenko Yu, Postnov D. Chaotic synchronization: applications to living systems. Singapore: World Scientific; 2002.
  8. Kuramoto Y. Chemical oscillations, waves and turbulence. Berlin: Springer-Verlag; 1984.
  9. Caldas IL, Tasson H. Limit cycles of periodically forced oscillations. Phys. Lett. A. 1989;135:264–266.
  10. Steeb WH, Kunick A. Chaos in limit-cycle systems with external periodic excitation. Int. J of Nonlinear Mechanics. 1987;22:349–361.
  11. Glass L, Sun J. Periodic forcing of a limit-cycle oscillator: Fixed points, Arnold tongues, and the global organization of bifurcations. Phys. Rev. 1994;50(6):5077–5084. DOI: 10.1103/physreve.50.5077.
  12. Pecora L, Carroll T. Synchronization in chaotic systems. Phys. Rev. Lett. 1990;64:821–824. DOI: 10.1103/PhysRevLett.64.821.
  13. Dykman G, Landa P, Neimark Y. Synchronizing the chaotic oscillations by external force. Chaos, Solitons and Fractals. 1991;1:339–353. DOI: 10.1016/0960-0779(91)90025-5.
  14. Anishchenko VS, Vadivasova TE, Postnov DE, Safonova MA. Synchronization of chaos. Int. J. Bifurcation and Chaos. 1992;2:633–644. DOI: 10.1142/S0218127492000756.
  15. Anishchenko VS, Silchenko AN, Khovanov IA. Synchronization of switching processes in coupled Lorenz systems. Phys. Rev. E. 1998;57:316–322. DOI: 10.1103/PhysRevE.57.316.
  16. Rosenblum M, Pikovsky A, Kurths J. Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 1996;76:1804–1807. DOI: 10.1103/PhysRevLett.76.1804.
  17. Kuznetsov SP. Dynamical Chaos: Course of Lectures. Moscow: Fizmatlit; 2001. (in Russian).
  18. Lorenz E. Deterministic Nonperiodic Flow. Journal of Atmospheric Sciences. 1963;20:130–141. DOI:10.1175/1520-0469(1963)020%3C0130:DNF%3E2.0.CO;2.
  19. Park EH, Zaks MA, Kurths J. Phase synchronization in the forced Lorenz system. Phys. Rev. E. 1999;60:6627–6638. DOI: 10.1103/physreve.60.6627.
  20. Kuznetsov YuI, Landa PS, Olkhovoi AF, Perminov SM. On the relation between the synchronization amplitude threshold and entropy in the stochastic self-oscillatory systems. Dokl. Akad. Nauk SSSR. 1985;281(2):291–294.
  21. Landa PS, Rendel YS, Sher VA. Synchronization in a Lorentz system. Izvestiya VUZ: Radiofizika. 1989;32(9):1172–1174.
  22. Afanasyev VV, Polsky IS. et al. Application of the Melnikov method for evaluating the effectiveness of the influence of external influences on complex nonlinear systems with strange attractors. Technical Physics Letters. 1997;23(23):40–45. (in Russian).
Received: 
24.01.2007
Accepted: 
05.06.2007
Published: 
31.07.2007
Short text (in English):
(downloads: 80)