scholarly journals Особенности обобщенной синхронизации в системах с запаздыванием

2019 ◽  
Vol 45 (11) ◽  
pp. 31
Author(s):  
А.Д. Плотникова ◽  
О.И. Москаленко
Keyword(s):  
Lyapunov Exponents ◽  
Generalized Synchronization ◽  
Interacting Systems ◽  
Synchronization Regime

Peculiarities of the generalized synchronization regime in unidirectionally coupled time-delayed generators are studied. Four different cases of interaction between systems characterized by different number of positive Lyapunov exponents are considered. The thresholds of the generalized synchronization regime onset is found to depend sufficiently on the degree of chaotic states of interacting systems, whereas the coupling between systems characterized by different number of positive Lyapunov exponents results in appearance of additional synchronous fields.

scholarly journals Метод определения характеристик перемежающейся обобщенной синхронизации на основе расчета локальных показателей Ляпунова

2020 ◽  
Vol 46 (16) ◽  
pp. 12
Author(s):  
О.И. Москаленко ◽  
Е.В. Евстифеев ◽  
А.А. Короновский
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
System Approach ◽  
Auxiliary System ◽  
Generalized Synchronization ◽  
Phase Detection ◽  
Unidirectional Coupling ◽  
Synchronization Regime ◽  
Good Agreement

Method for the laminar and turbulent phase detection in coupled dynamical systems being near the boundary of the generalized synchronization regime based on the calculation of local Lyapunov exponents has been proposed. The efficiency of the method has been testified using the systems with unidirectional coupling allowing the analysis of intermittency by the auxiliary system approach. The results of both methods have been compared with each other, a good agreement between them has been obtained.

scholarly journals Метод диагностики обобщенной синхронизации в системах со сложной топологией хаотического аттрактора

2018 ◽  
Vol 44 (19) ◽  
pp. 87
Author(s):  
О.И. Москаленко ◽  
В.А. Ханадеев ◽  
А.А. Короновский
Keyword(s):  
Numerical Simulation ◽  
Phase Space ◽  
Lyapunov Exponent ◽  
Chaotic Attractor ◽  
Diagnostic Technique ◽  
Generalized Synchronization ◽  
Chaotic State ◽  
Interacting Systems ◽  
Lyapunov Exponent Spectrum ◽  
Good Agreement

AbstractA diagnostic technique is proposed for the mode of generalized synchronization in systems with a complex chaotic attractor topology based on consideration of tubes of trajectories in the phase space of interacting systems. The method functionality is tested by the numerical simulation of two mutually coupled modified Lorentz systems: one in the chaotic state, and another in the hyperchaotic state. The results are compared to the data obtained by calculating the Lyapunov exponent spectrum and show good agreement.

scholarly journals Properties of generalized synchronization in smooth and non-smooth identical oscillators

2020 ◽  
Vol 229 (12-13) ◽  
pp. 2151-2165
Author(s):  
M. Balcerzak ◽  
A. Chudzik ◽  
A. Stefanski
Keyword(s):  
Fractal Dimension ◽  
Lyapunov Exponents ◽  
Lorenz System ◽  
Generalized Synchronization ◽  
Parameter Mismatch ◽  
Synchronous State ◽  
Chua Circuit ◽  
Analysis Tools ◽  
The Stability

Abstract This paper deals with the phenomenon of the GS only in the context of unidirectional connection between identical exciter and receivers. A special attention is focused on the properties of the GS in coupled non-smooth Chua circuits. The robustness of the synchronous state is analyzed in the presence of slight parameter mismatch. The analysis tools are transversal and response Lyapunov exponents and fractal dimension of the attractor. These studies show differences in the stability of synchronous states between smooth (Lorenz system) and non-smooth (Chua circuit) oscillators.

scholarly journals Метод определения характеристик перемежающейся обобщенной синхронизации, основанный на вычислении вероятности наблюдения синхронного режима

2022 ◽  
Vol 48 (2) ◽  
pp. 3
Author(s):  
О.И. Москаленко ◽  
А.А. Короновский ◽  
А.О. Сельский ◽  
Е.В. Евстифеев
Keyword(s):  
Chaotic Synchronization ◽  
Coupled Systems ◽  
The Other ◽  
Generalized Synchronization ◽  
Synchronization Regime

Method to define the characteristic phases in the behavior of unidirectionally coupled systems being near the boundary of the generalized chaotic synchronization regime onset, based on calculation of the probability of the synchronous regime observation in ensemble of coupled systems is proposed. Using the example of unidirectionally coupled Rössler systems in the band chaos regime we show its efficiency in comparison with the other known methods for detection the characteristics of intermittent generalized synchronization.

scholarly journals Корректность определения характеристик перемежающейся обобщенной синхронизации при использовании только одной переменной ведомой и вспомогательной систем

2020 ◽  
Vol 46 (7) ◽  
pp. 48 ◽  
Author(s):  
А.А. Короновский ◽  
О.И. Москаленко ◽  
А.О. Сельский
Keyword(s):  
The State ◽  
Auxiliary System ◽  
Generalized Synchronization ◽  
Correct Determination ◽  
Synchronization Regime

Method for detection of characteristic phases of behavior in the intermittent generalized synchronization regime based on the use of an auxiliary system is considered. It is found that for the correct determination of the type of intermittency realized in the system, it is sufficient to use the only one variable characterizing the state of this system.

Lyapunov Exponents

2016 ◽  
Author(s):  
Arkady Pikovsky ◽  
Antonio Politi
Keyword(s):  
Lyapunov Exponents

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

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