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

E. D. Illarionova ; O. I. Moskalenko

Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 31 (2023) no. 5, pp. 566-574.

Résumé

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.

Détail

Keywords: noise-induced synchronization, generalized synchronization, multistability, white noise, intermittency.

Bibliographie

[1] Pikovsky A., Rosenblum M., Kurths J., Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge University Press, New York, 2001, 432 pp. | DOI

[2] Anishchenko V. S., Astakhov V., Vadivasova T., Neiman A., Schimansky-Geier L., Nonlinear Dynamics of Chaotic and Stochastic Systems: Tutorial and Modern Developments, Springer-Verlag, Berlin Heidelberg, 2007, 446 pp. | DOI

[3] Balanov A., Janson N., Postnov D., Sosnovtseva O., Synchronization: From Simple to Complex, Springer-Verlag, Berlin Heidelberg, 2009, 426 pp. | DOI

[4] Boccaletti S., Pisarchik A. N., del Genio C. I., Amann A., Synchronization: From Coupled Systems to Complex Networks, Cambridge University Press, Cambridge, 2018, 264 pp. | DOI

[5] Boccaletti S., Kurths J., Osipov G., Valladares D. L., Zhou C. S., “The synchronization of chaotic systems”, Physics Reports, 366:1–2 (2002), 1–101 | DOI

[6] Rosenblum M. G., Pikovsky A. S., Kurths J., “Synchronization approach to analysis of biological systems”, Fluctuation and Noise Letters, 4:1 (2004), L53–L62 | DOI

[7] Koronovskii A. A., Moskalenko O. I., Khramov A. E., “O primenenii khaoticheskoi sinkhronizatsii dlya skrytoi peredachi informatsii”, Uspekhi fizicheskikh nauk, 179:12 (2009), 1281–1310 | DOI

[8] Zhang F., Chen G., Li C., Kurths J., “Chaos synchronization in fractional differential systems”, Phil. Trans. R. Soc. A, 371:1990 (2013), 20120155 | DOI

[9] Strelkova G. I., Anischenko V. S., “Prostranstvenno-vremennye struktury v ansamblyakh svyazannykh khaoticheskikh sistem”, Uspekhi fizicheskikh nauk, 190:2 (2020), 160–178 | DOI

[10] Toral R., Mirasso C. R., Hernández-García E., Piro O., “Analytical and numerical studies of noise-induced synchronization of chaotic systems”, Chaos, 11:3 (2001), 665–673 | DOI

[11] Wang Y., Lai Y.-C., Zheng Z., “Route to noise-induced synchronization in an ensemble of uncoupled chaotic systems”, Phys. Rev. E, 81:3 (2010), 036201 | DOI

[12] Moskalenko O. I., Koronovskii A. A., Shurygina S. A., “Peremezhayuscheesya povedenie na granitse indutsirovannoi shumom sinkhronizatsii”, ZhTF, 81:9 (2011), 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, 31:8 (2021), 083106 | DOI

[14] Moskalenko O. I., Evstifeev E. V., “O suschestvovanii multistabilnosti vblizi granitsy obobschennoi sinkhronizatsii v odnonapravlenno svyazannykh sistemakh so slozhnoi topologiei attraktora”, Izvestiya vuzov. PND, 30:6 (2022), 676–684 | DOI

[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, 354:5–6 (2006), 423–427 | DOI