Multistability near the boundary of noise-induced synchronization in ensembles of uncoupled chaotic systems

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Abstract

The aim of this work is to study the possibility of the existence of multistability near the boundary of noise-induced synchronization in chaotic continuous and discrete systems. Ensembles of uncoupled Lorenz systems and logistic maps being under influence of a common source of white noise have been chosen as an object under study. Methods. The noise-induced synchronization regime detection has been performed by means of direct comparison of the system states being under influence of the common noise source and by calculation of the synchronization error. To determine the presence of multistability near the boundary of this regime, the multistability measure has been calculated and its dependence on the noise intensity has been obtained. In addition, for fixed moments of time, the basins of attraction of the synchronous and asynchronous regimes have been received for one of the systems driven by noise for fixed initial conditions of the other system. The result of the work is a proof of the presence of multistability near the boundary of noise-induced synchronization. Conclusion. It is shown that the regime of intermittent noise-induced synchronization, as well as the regime of intermittent generalized synchronization, is characterized by multistability, which manifests itself in this case as the existence in the same time interval of the synchronous behavior in one pair of systems being under influence of a common noise source, whereas in the other pair the asynchronous behavior is observed. The found effect is typical for both flow systems and discrete maps being under influence of a common noise source. It can find an application in the information and telecommunication systems for improvement the methods for secure information transmission based on the phenomenon of chaotic synchronization.

About the authors

Ekaterina Dmitrievna Illarionova

Saratov State University

ORCID iD: 0000-0003-1912-863X
ul. Astrakhanskaya, 83, Saratov, 410012, Russia

Olga Igorevna Moskalenko

Saratov State University

ORCID iD: 0000-0001-5727-5169
Scopus Author ID: 10038769200
ResearcherId: D-4420-2011
ul. Astrakhanskaya, 83, Saratov, 410012, Russia

References

  1. Pikovsky A., Rosenblum M., Kurths J. Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge: Cambridge University Press, 2001. 432 p. doi: 10.1017/CBO9780511755743.
  2. Anishchenko V. S., Astakhov V., Vadivasova T., Neiman A., Schimansky-Geier L. Nonlinear Dynamics of Chaotic and Stochastic Systems: Tutorial and Modern Developments. Berlin Heidelberg: Springer-Verlag, 2007. 446 p. doi: 10.1007/978-3-540-38168-6.
  3. Balanov A., Janson N., Postnov D., Sosnovtseva O. Synchronization: From Simple to Complex. Berlin Heidelberg: Springer-Verlag, 2009. 426 p. doi: 10.1007/978-3-540-72128-4.
  4. Boccaletti S., Pisarchik A. N., del Genio C. I., Amann A. Synchronization: From Coupled Systems to Complex Networks. Cambridge: Cambridge University Press, 2018. 264 p. doi: 10.1017/978110 7297111.
  5. Boccaletti S., Kurths J., Osipov G., Valladares D. L., Zhou C. S. The synchronization of chaotic systems // Physics Reports. 2002. Vol. 366, no. 1–2. P. 1–101. doi: 10.1016/S0370-1573(02)00137-0.
  6. Rosenblum M. G., Pikovsky A. S., Kurths J. Synchronization approach to analysis of biological systems // Fluctuation and Noise Letters. 2004. Vol. 4, no. 1. P. L53–L62. doi: 10.1142/S0219477 504001653.
  7. Короновский А. А., Москаленко О. И., Храмов А. Е. О применении хаотической синхронизации для скрытой передачи информации // Успехи физических наук. 2009. Т. 179, № 12. С. 1281–1310. doi: 10.3367/UFNr.0179.200912c.1281.
  8. Zhang F., Chen G., Li C., Kurths J. Chaos synchronization in fractional differential systems // Phil. Trans. R. Soc. A. 2013. Vol. 371, no. 1990. P. 20120155. doi: 10.1098/rsta.2012.0155.
  9. Стрелкова Г. И., Анищенко В. С. Пространственно-временные структуры в ансамблях связанных хаотических систем // Успехи физических наук. 2020. Т. 190, № 2. С. 160–178. doi: 10.3367/UFNr.2019.01.038518.
  10. Toral R., Mirasso C. R., Hernandez-Garcia E., Piro O. Analytical and numerical studies of noise-induced synchronization of chaotic systems // Chaos. 2001. Vol. 11, no. 3. P. 665–673. doi: 10.1063/1.1386397.
  11. Wang Y., Lai Y.-C., Zheng Z. Route to noise-induced synchronization in an ensemble of uncoupled chaotic systems // Phys. Rev. E. 2010. Vol. 81, no. 3. P. 036201. doi: 10.1103/PhysRevE.81.036201.
  12. Москаленко О. И., Короновский А. А., Шурыгина С. А. Перемежающееся поведение на границе индуцированной шумом синхронизации // ЖТФ. 2011. Т. 81, № 9. С. 150–153.
  13. Moskalenko O. I., Koronovskii A. A., Selskii A. O., Evstifeev E. V. On multistability near the boundary of generalized synchronization in unidirectionally coupled chaotic systems // Chaos. 2021. Vol. 31, no. 8. P. 083106. doi: 10.1063/5.0055302.
  14. Москаленко О. И., Евстифеев Е. В. О существовании мультистабильности вблизи границы обобщенной синхронизации в однонаправленно связанных системах со сложной топологией аттрактора // Известия вузов. ПНД. 2022. Т. 30, № 6. С. 676–684. doi: 10.18500/0869-6632- 003013.
  15. Hramov A. E., Koronovskii A. A., Moskalenko O. I. Are generalized synchronization and noise induced synchronization identical types of synchronous behavior of chaotic oscillators? // Phys. Lett. A. 2006. Vol. 354, no. 5–6. P. 423–427. doi: 10.1016/j.physleta.2006.01.079.

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