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

For citation:

Moskalenko O. I., Evstifeev E. V. On existence of multistability near the boundary of generalized synchronization in unidirectionally coupled systems with complex topology of attractor. Izvestiya VUZ. Applied Nonlinear Dynamics, 2022, vol. 30, iss. 6, pp. 676-684. DOI: 10.18500/0869-6632-003013, EDN: LSEQWO

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Language: 
Russian
Heading: 
Bifurcation in Dynamical Systems. Deterministic Chaos. Quantum Chaos.
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-003013
EDN: 
LSEQWO

On existence of multistability near the boundary of generalized synchronization in unidirectionally coupled systems with complex topology of attractor

Autors: 
Moskalenko Olga Igorevna, Saratov State University
Evstifeev Evgeniy Valentinovich, Saratov State University
Abstract: 

Aim of this work is to study the possibility of existence of multistability near the boundary of generalized synchronization in systems with complex attractor topology. Unidirectionally coupled Lorentz systems have been chosen as an object of study, and a modified auxiliary system method has been used to detect the presence of the synchronous regime. Result of the work is a proof of the presence of multistability near the boundary of generalized synchronization in unidirectionally coupled systems with a complex topology of attractor. For this purpose, the basins of attraction of the synchronous and asynchronous states of interacting Lorenz systems have been obtained for the value of the coupling parameter corresponding to the realization of the intermittent generalized synchronization regime in the system under study, and the dependence of the multistability measure on the value of the coupling parameter has also been calculated. It is shown that in the regime of intermittent generalized synchronization the measure of multistability turns out to be positive, which is an additional confirmation of the presence of multistability in this case.

Key words: 
generalized synchronization
multistability
systems with complex topology of attractor
intermittency
auxiliary system approach
Acknowledgments: 
This work was financially supported 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-18.2022.1.2)
Reference: 
  1. Pisarchik AN, Feudel U. Control of multistability. Physics Reports. 2014;540(4):167–218. DOI: 10.1016/j.physrep.2014.02.007.
  2. Attneave F. Multistability in perception. Sci. Am. 1971;225(6):63–71. DOI: 10.1038/ scientificamerican1271-62.
  3. Bezruchko BP, Seleznev EP, Smirnov EV. Evolution of basins of attractors of symmetrically coupled systems with period doubling. Tech. Phys. Lett. 1995;21(8):12–17 (in Russian).
  4. Eschenazi E, Solari HG, Gilmore R. Basins of attraction in driven dynamical systems. Phys. Rev. A. 1989;39(5):2609–2627. DOI: 10.1103/PhysRevA.39.2609.
  5. Moreno-Bote R, Rinzel J, Rubin N. Noise-induced alternations in an attractor network model of perceptual bistability. Journal of Neurophysiology. 2007;98(3):1125–1139. 10.1152/jn.00116. 2007.
  6. Feudel U. Complex dynamics in multistable systems. International Journal of Bifurcation and Chaos. 2008;18(6):1607–1626. DOI: 10.1142/S0218127408021233.
  7. Pozdnyakov MV, Savin AV. Multistable regimes in asymmetrically coupled period-doubling systems. Izvestiya VUZ. Applied Nonlinear Dynamics. 2010;18(5):44–53 (in Russian). DOI: 10.18500/0869-6632-2010-18-5-44-53.
  8. Postnov DE, Vadivasova TE, Sosnovtseva OV, Balanov AG, Anishchenko VS, Mosekilde E. Role of multistability in the transition to chaotic phase synchronization. Chaos. 1999;9(1):227–232. DOI: 10.1063/1.166394.
  9. Carvalho R, Fernandez B, Vilela Mendes R. From synchronization to multistability in two coupled quadratic maps. Phys. Lett. A. 2001;285(5–6):327–338. DOI: 10.1016/S0375-9601(01)00370-X.
  10. Astakhov V, Shabunin A, Uhm W, Kim S. Multistability formation and synchronization loss in coupled Henon maps: Two sides of the single bifurcational mechanism. Phys. Rev. E. 2001;63(5):056212. DOI: 10.1103/PhysRevE.63.056212.
  11. Pikovsky A, Popovych O, Maistrenko Y. Resolving clusters in chaotic ensembles of globally coupled identical oscillators. Phys. Rev. Lett. 2001;87(4):044102. DOI: 10.1103/PhysRevLett. 87.044102.
  12. Campos-Mej´ıa A, Pisarchik AN, Arroyo-Almanza DA. Noise-induced on–off intermittency in mutually coupled semiconductor lasers. Chaos, Solitons & Fractals. 2013;54:96–100. DOI: 10.1016/ j.chaos.2013.06.006.
  13. 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.
  14. Koronovskii AA, Moskalenko OI, Hramov AE. Nearest neighbors, phase tubes, and generalized synchronization. Phys. Rev. E. 2011;84(3):037201. DOI: 10.1103/PhysRevE.84.037201.
  15. Moskalenko OI, Koronovskii AA, Hramov AE, Boccaletti S. Generalized synchronization in mutually coupled oscillators and complex networks. Phys. Rev. E. 2012;86(3):036216. DOI: 10.1103/ PhysRevE.86.036216.
  16. Hramov AE, Koronovskii AA. Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators. Europhys. Lett. 2005;70(2):169–175. DOI: 10.1209/epl/i2004-10488-6.
  17. Koronovskii AA, Moskalenko OI, Pivovarov AA, Evstifeev EV. Intermittent route to generalized synchronization in bidirectionally coupled chaotic oscillators. Chaos. 2020;30(8):083133. DOI: 10.1063/5.0007156.
  18. Moskalenko OI, Koronovskii AA, Khanadeev VA. Method for characteristic phase detection in systems with complex topology of attractor being near the boundary of generalized synchronization. Izvestiya VUZ. Applied Nonlinear Dynamics. 2020;28(3):274–281 (in Russian). DOI: 10.18500/ 0869-6632-2020-28-3-274-281.
  19. Koronovskii AA, Moskalenko OI, Pivovarov AA, Khanadeev VA, Hramov AE, Pisarchik AN. Jump intermittency as a second type of transition to and from generalized synchronization. Phys. Rev. E. 2020;102(1):012205. DOI: 10.1103/PhysRevE.102.012205.
  20. Moskalenko OI, Koronovskii AA, Selskii AO, Evstifeev EV. On multistability near the boundary of generalized synchronization in unidirectionally coupled chaotic systems. Chaos. 2021;31(8):083106. DOI: 10.1063/5.0055302.
  21. Moskalenko OI, Koronovskii AA, Selskii AO, Evstifeev EV. A method to detect the characteristics of intermittent generalized synchronization based on calculation of probability of the synchronous regime observation. Tech. Phys. Lett. 2022;48(1):49–52. DOI: 10.21883/PJTF.2022.02.51910.18985.
  22. Zheng Z, Wang X, Cross MC. Transitions from partial to complete generalized synchronizations in bidirectionally coupled chaotic oscillators. Phys. Rev. E. 2002;65(5):056211. DOI: 10.1103/ PhysRevE.65.056211.
  23. Abarbanel HDI, Rulkov NF, Sushchik MM. Generalized synchronization of chaos: The auxiliary system approach. Phys. Rev. E. 1996;53(5):4528–4535. DOI: 10.1103/PhysRevE.53.4528.
Received: 
03.06.2022
Accepted: 
06.07.2022
Available online: 
14.10.2022
Published: 
30.11.2022
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