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


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Vadivasova T. E., Zaharova A. S. Spectral analysis of oscillations in the system of coupled chaotic self-sustained oscillators. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 4, pp. 16-25. DOI: 10.18500/0869-6632-2007-15-4-16-25

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Russian
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Article
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537.86

Spectral analysis of oscillations in the system of coupled chaotic self-sustained oscillators

Autors: 
Vadivasova Tatjana Evgenevna, Saratov State University
Zaharova Anna Sergeevna, Technische Universitßt Berlin
Abstract: 

Spectra of oscillations in the system of two coupled self-sustained chaotic oscillators are investigated in present work. The relation between spectra and partial effective phase diffusion coefficients is determined. We follow the evolution of spectra and diffusion coefficients from the asynchronous regime to the regime of synchronous chaos. The analogy between spectral characteristics of coupled chaotic oscillators and noisy coupled periodic oscillators is drawn.  

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Reference: 
  1. Farmer JD. Spectral broadening of period–doubling bifurcation sequences. Phys. Rev. Lett. 1981;47(3):179-182.
  2. Pikovsky A, Rosenblum M, Kurts Yu. Synchronization: A fundamental nonlinear phenomenon. Moscow: Tehnosphera; 2003. 493 p.
  3. Anishchenko VS, Vadivasova TE, Kurths J, Okrokvertskhov GA, Strelkova GI. Autocorrelation function and spectral linewidth of spiral chaos in a physical experiment. Phys. Rev. E. 2004;69:036215. DOI: 10.1103/PhysRevE.69.036215.
  4. Anishchenko VS, Okrokvertskhov GA, Vadivasova TE, Strelkova GI. Mixing and spectral-correlation properties of chaotic and stochastic systems: numerical and physical experiments. New Journal of Physics. 2005;7:76. DOI: 10.1088/1367-2630/7/1/076.
  5. Anishchenko VS, Vadivasova TE, Okrokvertskhov GA, Strelkova GI. Correlation analysis of deterministic and noisy chaos. Journal of Communications Technology and Electronics. 2003;48(7):750–760.
  6. Vadivasova TE, Anishchenko VS. Relationship between frequency and phase characteristics of chaos: Two criteria of synchronization. Journal of Communications Technology and Electronics. 2004;49(1):69–75.
  7. Anishchenko VS, Vadivasova TE, Kopeikin AS, Kurths J, Strelkova GI. Effect of noise on the relaxation to an invariant probability measure of nonhyperbolic chaotic attractors. Phys. Rew. Lett. 2001;87(5):4101.
  8. Anishchenko VS, Vadivasova TE, Kopeikin AS, Kurths J, Strelkova GI. Peculiarities of the relaxation to an invariant probability measure of nonhyperbolic chaotic attractors in the presence of noise. Phys. Rev. E. 2002;65(3):036206. DOI: 10.1103/PhysRevE.65.036206.
  9. Anishchenko VS, Vadivasova TE, Strelkova GI, Okrokvertskhov GA. Statistical properties of deterministic and noisy chaotic systems. Izvestiya VUZ. Applied Nonlinear Dynamics. 2003;11(3):4–19.
  10. Anishchenko VS, Astakhov VV, Vadivasova TE, Neiman AB, Strelkova GI, Shimanskii-Gaier L. Nonlinear effects in chaotic and stochastic systems. Moscow-Izhevsk: Institute of Computer Sciences; 2003. 535 pp.
  11. Pikovsky A, Osipov G, Rosenblum M, Zaks M, Kurths J. Attractor – repeller collision and eyelet intermittency at the transition to phase synchronization. Phys. Rev. Lett. 1997;79:47–50. DOI: 10.1103/PhysRevLett.79.47.
  12. Rossler OE. An equation for continuous chaos. Phys. Lett. A. 1976;57:397–398. DOI: 10.1016/0375-9601(76)90101-8.
  13. Stratonovich RL. Selected issues of the theory of fluctuations in radio engineering. Moscow: Sov. Radio; 1961. (in Russian).
  14. Malakhov AN. Fluctuations in Self-Oscillating Systems. Moscow: Nauka; 1968. (in Russian).
  15. Landa PS. Self-Oscillation in Systems with Finite Number of Degress of Freedom. Moscow: Nauka; 1980. (in Russian).
Received: 
02.03.2007
Accepted: 
02.03.2007
Published: 
31.07.2007
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