Geodesic
Intermittent behavior near the boundary of generalized synchronization in unidirectionally coupled time-delayed systems
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 33 (2025) no. 1, pp. 9-18.

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The aim of the work is an analysis of characteristics of intermittent behavior taking place near the boundary of generalized synchronization in unidirectionally coupled time-delayed generators. The case of interaction of systems characterized by different numbers of positive Lyapunov exponents is considered. To determine the lengths of characteristic phases of the system behavior the auxiliary system method has been used. The result of the work is the determination of the type of intermittency taking place near the boundary of generalized synchronization. In this case by calculation the statistical characteristics of the laminar phase lengths (distributions of the laminar phase lengths and the dependencies of the mean lengths of the laminar phases on the criticality parameters) it has been found that near the boundary of the synchronous regime the on-off intermittency is observed. It has been shown that the intermittent generalized synchronization in time-delayed systems is characterized by multistability. For these purposes a time-averaged measure of multistability depending on the value of the coupling parameter between systems has been calculated and compared with the behavior of the spectrum of Lyapunov exponents. It has been found that the multistability measure can be used to detect the generalized synchronization in time-delayed systems.  
Keywords: time-delayed systems, unidirectional coupling, generalized synchronization, on-off intermittency, multistability, probability of observation the turbulent phase 
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O. I. Moskalenko; V. A. Khanadeev. Intermittent behavior near the boundary of generalized synchronization in unidirectionally coupled time-delayed systems. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 33 (2025) no. 1, pp. 9-18. http://geodesic.mathdoc.fr/item/IVP_2025_33_1_a1/

[1] Shen Y., Liu X., “Generalized synchronization of delayed complex-valued dynamical networks via hybrid control”, Communications in Nonlinear Science and Numerical Simulation, 118 (2023), 107057 | DOI

[2] Xing Y., Dong W., Zeng J., Guo P., Zhang J., Ding Q., “Study of generalized chaotic synchronization method incorporating error-feedback coefficients”, Entropy, 25:5 (2023), 818 | DOI

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

[4] Starodubov A. V., Koronovskii A. A., Khramov A. E., Zharkov Yu. D., Dmitriev B. S., “Issledovanie obobschennoi sinkhronizatsii v sisteme dvukh svyazannykh klistronnykh avtogeneratorov khaosa”, Pisma v ZhTF, 33:14 (2007), 58–65

[5] Khramov A. E., Frolov N. S., Maksimenko V. A., Kurkin S. A., Kazantsev V. B., Pisarchik A. N., “Funktsionalnye seti golovnogo mozga: ot vosstanovleniya svyazei do dinamicheskoi integratsii”, UFN, 191:6 (2021), 614–650 | DOI

[6] Rulkov N. F., Sushchik M. M., Tsimring L. S. and Abarbanel H. D. I., “Generalized synchronization of chaos in directionally coupled chaotic systems”, Phys. Rev. E, 51 (1995), 980–994 | DOI

[7] Moskalenko O. I., Koronovskii A. A., Hramov A. E., Boccaletti S., “Generalized synchronization in mutually coupled oscillators and complex networks”, Phys. Rev. E, 86 (2012), 036216 | DOI

[8] Pyragas K., “Weak and strong synchronization of chaos”, Phys. Rev. E, 54:5 (1996), R4508–R4511 | DOI

[9] Hramov A. E., Koronovskii A. A., “Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators”, Europhysics Letters, 70:2 (2005), 169-175 | DOI

[10] Koronovskii A. A., Moskalenko O. I., Pivovarov A. A., Khanadeev V. A., Hramov A. E., Pisarchik A. N., “Jump intermittency as a second type of transition to and from generalized synchronization”, Phys. Rev. E, 102 (2020), 012205 | DOI

[11] Koronovskii A.A., Moskalenko O.I., Pivovarov A. A., Evstifeev E. V., “Intermittent route to generalized synchronization in bidirectionally coupled chaotic oscillators”, Chaos, 30 (2020), 083133 | DOI

[12] Popov P. V., “Peremezhayuschayasya obobschennaya sinkhronizatsiya v raspredelennykh avtokolebatelnykh sredakh na primere kompleksnykh uravnenii Ginzburga–Landau”, Pisma v ZhTF, 33:18 (2007), 61–69

[13] Ponomarenko V. I., Prokhorov M. D., “Vydelenie informatsionnoi komponenty khaoticheskogo signala sistemy s zapazdyvaniem”, Pisma v ZhTF, 28:16 (2002), 37–44

[14] Karavaev A. S., Ponomarenko V. I., Prokhorov M. D., “Vosstanovlenie modelei skalyarnykh sistem s zapazdyvaniem po vremennym ryadam”, Pisma v ZhTF, 27:10 (2001), 43–51

[15] Koloskova A. D., Moskalenko O. I., Koronovskii A. A., “Metod rascheta spektra pokazatelei Lyapunova dlya sistem s zapazdyvaniem”, Pisma v ZhTF, 44:9 (2018), 19–25 | DOI

[16] Plotnikova A. D., Moskalenko O. I., “Osobennosti obobschennoi sinkhronizatsii v sistemakh s zapazdyvaniem”, Pisma v ZhTF, 45:11 (2019), 31–33 | DOI

[17] Abarbanel H. D. I., Rulkov N. F., Sushchik M., “Generalized synchronization of chaos: The auxiliary system approach”, Phys. Rev. E, 53:5 (1996), 4528–4535 | DOI

[18] Ott E., Sommerer J. C., “Blowout bifurcations: the occurrence of riddled basins and on-off intermittency”, Phys. Lett. A, 188:1 (1994), 39 | DOI

[19] Moskalenko O. I., Koronovskii A. A., Selskii A. A., Evstifeev E. V., “On multistability near the boundary of generalized synchronization in unidirectionally coupled chaotic systems”, Chaos, 31:8 (2021), 083106 | DOI

[20] 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

[21] Moskalenko O. I., Evstifeev E. V., Koronovskii A. A., “Metod opredeleniya kharakteristik peremezhayuscheisya obobschennoi sinkhronizatsii na osnove rascheta lokalnykh pokazatelei Lyapunova”, Pisma v ZhTF, 46:16 (2020), 12 | DOI