Izvestiya of Saratov University.

Physics

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

For citation:

Moskalenko O. I., Hanadeev V. A. Influence of noise on generalized synchronization in systems with a complex topology of attractor. Izvestiya of Saratov University. Physics , 2021, vol. 21, iss. 3, pp. 233-241. DOI: 10.18500/1817-3020-2021-21-3-233-241, EDN: VMCYEM

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.08.2021
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Language: 
Russian
Heading: 
Radiophysics, electronics, acoustics
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/1817-3020-2021-21-3-233-241
EDN: 
VMCYEM

Influence of noise on generalized synchronization in systems with a complex topology of attractor

Autors: 
Moskalenko Olga Igorevna, Saratov State University
Hanadeev Vladislav Andreevich, Saratov State University
Abstract: 

Background and Objectives: The goal of the paper is to study the influence of noise on generalized synchronization in unidirectionally coupled systems with a complex topology of attractor. As the systems under study, two models of chaotic systems with two-sheeted topologies of attractors such as Lorenz and Chen systems are considered. Materials and Methods: For the synchronous regime detection the method of calculating the spectrum of Lyapunov exponents for coupled systems and the auxiliary system approach are used. Results: It has been shown that the dependences of the threshold for the onset of the generalized synchronization regime on the noise intensity do not practically change both for Lorenz and Chen systems. Conclusion: Using the examples of Lorenz oscillators and Chen systems we have found that the generalized synchronization regime in systems with a complex topology of attractor is stable to external noise. This behavior of systems is determined by the weak influence of noise on the structure of attractors of interacting systems, which is confirmed by constructing their phase portraits for different values of the noise intensity

Key words: 
generalized synchronization
auxiliary system approach
calculation of the spectrum of Lyapunov exponents
noise
complex topology of attractor
Acknowledgments: 
This work was funded by the Grant Council of the President of the Russian Federation for the state support of young Russian scientists – doctors of sciences (project No. MD-21.2020.2).
Reference: 
  1. Pikovsky A., Rosenblum M., Kurths J. Synchronization: A universal concept in nonlinear sciences. New York, Cambridge University Press, 2001. 411 p. https://doi.org/10.1017/CBO9780511755743
  2. Boccaletti S., Kurths J., Osipov G., Valladares D. L., Zhou C. S. The synchronization of chaotic systems. Phys. Rep., 2002, vol. 366, iss. 1–2, pp. 1–101. https://doi.org/10.1016/S0370-1573(02)00137-0
  3. Anishchenko V. S. Complex Oscillations in Simple Systems. Mechanisms of Occurrence, Structure and Properties of Dynamic Chaos in Radiophysical Systems. 2nd ed. Moscow, URSS Publ., 2009. 320 p. (in Russian).
  4. Blekhman I. I. Synchronization in Science and Technology. Moscow, URSS Publ., 2021. 440 p. (in Russian).
  5. Kocarev L., Parlitz U. General approach for chaotic synchronization with applications to communication. Phys. Rev. Lett., 1995, vol. 74, iss. 25, pp. 5028–5031. https://doi.org/10.1103/PhysRevLett.74.5028
  6. Chub R. O., Ponomarenko V. I., Prokhorov M. D. Method for Information Transmission Using a Predictive Model in Coupled Time-delay Systems. Izv. Saratov Univ. Physics, 2018, vol. 18, iss. 2, pp. 84–91 (in Russian). https://doi.org/10.18500/1817-3020-2018-18-2-84-91
  7. Kul’minskii D. D., Ponomarenko V. I., Karavaev A. S., Prokhorov M. D. Noise-resistant system of concealed information transfer on a chaotic delayed feedback oscillator with switchable delay time. Technical Physics, 2016, vol. 61, iss. 5, pp. 639–647. https://doi.org/10.1134/S1063784216050121
  8. Pavlov A., Sosnovtseva O., Ziganshin A., HolsteinRathlou N.-H., Mosekilde E. Multiscality in the dynamics of coupled chaotic systems. Phys. A, 2002, vol. 316, iss. 1–4, pp. 233–249. https://doi.org/10.1016/S0378-4371(02)01202-5
  9. Dmitriev B. S., Hramov A. E., Koronovskii A. A., Starodubov A. V., Trubetskov D. I., Zharkov Y. D. First experimental observation of generalized synchronization phenomena in microwave oscillators. Phys. Rev. Lett., 2009, vol. 102, iss. 7, pp. 074101. https://doi.org/10.1103/PhysRevLett.102.074101
  10. Anishchenko V. S., Postnov D. E. Effect of the basic frequency locking of chaotic auto-oscillations - synchronization of strange attractors. Pisma v zhurnal tekhnicheskoi fiziki, 1988, vol. 14, iss. 6. pp. 569–573 (in Russian).
  11. Pecora L. M., Carroll T. L. Synchronization in chaotic systems. Phys. Rev. Lett., 1990, vol. 64, iss. 8, pp. 821–824. https://doi.org/10.1103/PhysRevLett.64.821
  12. Carroll T. L., Pecora L. M. Synchronizing chaotic circuits. IEEE Trans. Circuits Syst., 1991, vol. 38, iss. 4, pp. 453–456. https://doi.org/10.1109/31.75404
  13. Rosenblum M. G., Pikovsky A. S., Kurths J. From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett., 1997, vol. 78, iss. 22, pp. 4193–4196. https://doi.org/10.1103/PhysRevLett.78.4193
  14. Rulkov N. F., Sushchik M. M., Tsimring L. S., Abarbanel H. D. I. Generalized synchronization of chaos in directionally coupled chaotic systems. Phys. Rev. E, 1995, vol. 51, iss. 2, pp. 980–994. https://doi.org/10.1103/PhysRevE.51.980
  15. Heagy J. F., Carroll T. L., Pecora L. M. Desynchronization by periodic orbits. Phys. Rev. E, 1995, vol. 52, iss. 2, pp. R1253–R1256. https://doi.org/10.1103/PhysRevE.52.R1253
  16. Zhou C., Kurths J., Kiss I. Z., Hudson J. L. Noiseenhanced phase synchronization of chaotic oscillators. Phys. Rev. Lett., 2002, vol. 89, iss. 1, pp. 014101. https://doi.org/10.1103/PhysRevLett.89.014101
  17. Moskalenko O. I., Hramov A. E., Koronovskii A. A., Ovchinnikov A.A. Effect of noise on generalized synchronization of chaos: Theory and experiment. Eur. Phys. J. B, 2011, vol. 82, iss. 1, pp. 69–82. https://doi.org/10.1140/epjb/e2011-11019-1
  18. Moskalenko O. I., Koronovskii A. A., Hramov A. E. Generalized synchronization of chaos for secure communication: Remarkable stability to noise. Phys. Lett. A, 2010, vol. 374, iss. 29, pp. 2925–2931. https://doi.org/10.1016/j.physleta.2010.05.024
  19. Khanadeev V. A., Moskalenko O. I., Koronovskii A. A. Intermittency near the boundary of generalized synchronization in systems with a complex topology of attractor. Bulletin of the Russian Academy of Sciences: Physics. 2021, vol. 85, iss. 2, pp. 192–195. https://doi.org/10.3103/S106287382102012X
  20. Pyragas K. Weak and strong synchronization of chaos. Phys. Rev. E, 1996, vol. 54, iss. 5, pp. R4508–R4511. https://doi.org/10.1103/PhysRevE.54.R4508
  21. Abarbanel H. D. I., Rulkov N. F., Sushchik M. M. Generalized synchronization of chaos: The auxiliary system approach. Phys. Rev. E, 1996, vol. 53, iss. 5, pp. 4528–4535. https://doi.org/10.1103/PhysRevE.53.4528
  22. Chen Z., Yang Y., Qi G., Yuan Z. A novel hyperchaos system only with one equilibrium. Phys. Lett. A, 2007, vol. 360, iss. 6, pp. 696–701. https://doi.org/10.1016/j.physleta.2006.08.085
  23. Nikitin N. N., Pervachev S. V., Razevig V. D. On computer solutiuon of stochastic differential equations for flow-up systems. Automation and Telemechanics, 1975, iss. 4, pp. 133–137 (in Russian).
  24. Hramov A. E., Koronovskii A. A. Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators. Europhys. Lett., 2005, vol. 70, iss. 2, pp. 169–175. https://doi.org/10.1209/epl/i2004-10488-6
Received: 
23.02.2021
Accepted: 
26.04.2021
Published: 
31.08.2021
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