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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     title = {Intermittent behavior near the boundary of generalized synchronization in unidirectionally coupled time-delayed systems},
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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/