Noise Influence on the Estimation of Characteristics of Intermittent Generalized Synchronization Using Local Lyapunov Exponents

2021 ◽  
pp. 161-168
Author(s):  
Evgeniy V. Evstifeev ◽  
Olga I. Moskalenko
Keyword(s):  
Lyapunov Exponents ◽  
Generalized Synchronization

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 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 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.

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.

scholarly journals Fluctuations of Lyapunov exponents in homogeneous and isotropic turbulence

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
Richard D. J. G. Ho ◽  
Andres Armua ◽  
Arjun Berera
Keyword(s):  
Lyapunov Exponents ◽  
Isotropic Turbulence ◽  
Homogeneous And Isotropic Turbulence

scholarly journals Hyperchaotic Image Encryption Based on Multiple Bit Permutation and Diffusion

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 510
Author(s):  
Taiyong Li ◽  
Duzhong Zhang
Keyword(s):  
Big Data ◽  
Lyapunov Exponents ◽  
Image Encryption ◽  
Hyperchaotic System ◽  
Encryption Scheme ◽  
Image Content ◽  
Image Security ◽  
Level Data ◽  
Different Types ◽  
And Diffusion

Image security is a hot topic in the era of Internet and big data. Hyperchaotic image encryption, which can effectively prevent unauthorized users from accessing image content, has become more and more popular in the community of image security. In general, such approaches conduct encryption on pixel-level, bit-level, DNA-level data or their combinations, lacking diversity of processed data levels and limiting security. This paper proposes a novel hyperchaotic image encryption scheme via multiple bit permutation and diffusion, namely MBPD, to cope with this issue. Specifically, a four-dimensional hyperchaotic system with three positive Lyapunov exponents is firstly proposed. Second, a hyperchaotic sequence is generated from the proposed hyperchaotic system for consequent encryption operations. Third, multiple bit permutation and diffusion (permutation and/or diffusion can be conducted with 1–8 or more bits) determined by the hyperchaotic sequence is designed. Finally, the proposed MBPD is applied to image encryption. We conduct extensive experiments on a couple of public test images to validate the proposed MBPD. The results verify that the MBPD can effectively resist different types of attacks and has better performance than the compared popular encryption methods.

On multistability near the boundary of generalized synchronization in unidirectionally coupled chaotic systems

2021 ◽  
Vol 31 (8) ◽  
pp. 083106
Author(s):  
Olga I. Moskalenko ◽  
Alexey A. Koronovskii ◽  
Anton O. Selskii ◽  
Evgeniy V. Evstifeev
Keyword(s):  
Chaotic Systems ◽  
Generalized Synchronization
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