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

For citation:

Danilov D. I., Koronovskii A. A. Spectral components’ behavior in coupled pierce diodes near the phase synchronization boundary. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 1, pp. 105-111. DOI: 10.18500/0869-6632-2012-20-1-105-111

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):
PDF icon 2012no1p105.pdf
(downloads: 158)
Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2012-20-1-105-111

Spectral components’ behavior in coupled pierce diodes near the phase synchronization boundary

Autors: 
Danilov Dmitrij Igorevich, Saratov State University
Koronovskii Aleksei Aleksandrovich, Saratov State University
Abstract: 

In this article we study the dynamics of two unidirectionally coupled Pierce diodes near the phase synchronization boundary in terms of synchronization of spectral components. We show that systems under consideration demonstrate self-similar behavior with any value of coupling strength within the region of our study. The results correlate with the data of the similar research for Rossler systems and circle map. 

Key words: 
Pierce diode
synchronization
spectral components
Fourier transform
intermittency
Reference: 
  1. Pikovsky A, Rosenblum M, Kurts Yu. Synchronization: A fundamental nonlinear phenomenon. Moscow: Tehnosphera; 2003. 493 p.
  2. Rosenblum MG, Pikovsky AS, Kurths J. Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 1996;76(11):1804–1807. DOI: 10.1103/PhysRevLett.76.1804.
  3. Rulkov NF, Sushchik MM, Tsimring LS, Abarbanel HDI. Generalized synchronization of chaos in directionally coupled chaotic systems. Phys. Rev. E. 1995;51(2):980–994. DOI: 10.1103/physreve.51.980.
  4. Rosenblum MG, Pikovsky AS, Kurths J. From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett. 1997;78(22):4193–4196. DOI: 10.1103/PhysRevLett.78.4193.
  5. Pecora LM, Carroll TL. Synchronization in chaotic systems. Phys. Rev. Lett. 1990;64(8):821–824. DOI: 10.1103/PhysRevLett.64.821.
  6. Hramov AE, Koronovskii AA. An approach to chaotic synchronization. Chaos. 2004;14(3):603–610. DOI: 10.1063/1.1775991.
  7. Hramov AE, Koronovskii AA, Levin YI. Synchronization of chaotic oscillator time scales. J. Exp. Theor. Phys. 2005;100:784–794. DOI: 10.1134/1.1926439.
  8. Hramov AE, Koronovskii AA, Kurovskaya MK, Moskalenko OI. Synchronization of spectral components and its regularities in chaotic dynamical systems. Phys. Rev. E. 2005;71(5):056204. DOI: 10.1103/PhysRevE.71.056204.
  9. Anishchenko VS, Vadivasova TE, Postnov DE, Safonova MA. Synchronization of chaos. Int. J. Bifurcation and Chaos. 1992;2:633–644. DOI: 10.1142/S0218127492000756.
  10. Boccaletti S, Valladares DL. Characterization of intermittent lag synchronization. Phys. Rev. E. 2000;62(5):7497–7500. DOI: 10.1103/physreve.62.7497.
  11. Pikovsky AS, Osipov GV, Rosenblum MG, Zaks M, Kurths J. Attractor–repeller collision and eyelet intermittency at the transition to phase synchronization. Phys. Rev. Lett. 1997;79(1):47–50. DOI: 10.1103/PhysRevLett.79.47.
  12. Hramov AE, Koronovskii AA, Kurovskaya MK, Moskalenko OI. Type-I intermittency with noise versus eyelet intermittency. Phys. Lett. A. 2011;375(15):1646–1652. DOI: 10.1016/j.physleta.2011.02.032.
  13. Danilov DI, Koronovskii AA. Universal regularity of the main spectral component synchronization of interacting oscillators. Bulletin of the Russian Academy of Sciences: Physics. 2011;75(12):1605–1608. DOI:  10.3103/S1062873811120100.
  14. Lectures on Microwave Electronics for Physicists. Vol. 1, 2. Moscow: Fizmatlit; 2003. (in Russian).
  15. Koronovskii AA, Moskalenko OI, Maksimenko VA, Hramov AE. Appearance of generalized synchronization in mutually coupled beam-plasma systems. Tech. Phys. Lett. 2011;37:610–613. DOI: 10.1134/S1063785011070108.
  16. Hramov AE, Rempen IS. Investigation of the complex dynamics and regime control in Pierce diode with the delay feedback. Int. J. Electronics. 2004;91(1):1–12. DOI: 10.1080/00207210310001658932.
  17. Pikovsky AS, Rosenblum MG, Kurths J. Phase synchronisation in regular and chaotic systems. Int. J. Bifurcation & Chaos. 2000;10(10):2291–2305. DOI: 10.1142/S0218127400001481.
  18. Hramov AE, Koronovskii AA, Kurovskaya MK. Zero Lyapunov exponent in the vicinity of the saddle-node bifurcation point in the presence of noise. Phys. Rev. E. 2008;78:036212. DOI: 10.1103/PhysRevE.78.036212.
Received: 
17.01.2012
Accepted: 
17.01.2012
Published: 
20.04.2012
Short text (in English):
PDF icon a2012no1p105.pdf
(downloads: 105)
  • 1968 reads