An analytic criterion for generalized synchronization in unidirectionally coupled systems based on the auxiliary system approach

2012 ◽  
Vol 22 (3) ◽  
pp. 033146 ◽  
Author(s):  
W. K. Wong ◽  
Bin Zhen ◽  
Jian Xu ◽  
Zhijie Wang
Keyword(s):  
System Approach ◽  
Coupled Systems ◽  
Auxiliary System ◽  
Generalized Synchronization ◽  
Analytic Criterion

GENERALIZED SYNCHRONIZATION OF CHAOS IN RCL-SHUNTED JOSEPHSON JUNCTIONS BY UNIDIRECTIONALLY COUPLING

2010 ◽  
Vol 24 (29) ◽  
pp. 5675-5682 ◽  
Author(s):  
YU-LING FENG ◽  
XI-HE ZHANG ◽  
ZHI-GANG JIANG ◽  
KE SHEN
Keyword(s):  
Lyapunov Exponent ◽  
Numerical Simulations ◽  
Josephson Junctions ◽  
System Approach ◽  
Chaotic Synchronization ◽  
Auxiliary System ◽  
Generalized Synchronization ◽  
Maximum Condition ◽  
Two Systems

This paper investigates chaotic synchronization in the generalized sense in two resistive-capacitive-inductive-shunted (RCL-shunted) Josephson junctions (RCLSJJs) by using the means of unidirectionally coupling. The numerical simulations confirm that the generalized synchronization of chaos in these two systems can be achieved with a suitable coupling intensity when the maximum condition Lyapunov exponent (MCLE) is negative. Also, the auxiliary system approach is used to detect the existence of the generalized synchronization.

scholarly journals On applicability of auxiliary system approach in complex network with ring topology

2019 ◽  
pp. 143-152 ◽  
Author(s):  
Volodymyr Lynnyk ◽  
Branislav Rehak ◽  
Sergej Celikovsky
Keyword(s):  
Numerical Simulations ◽  
Complex Network ◽  
System Approach ◽  
Chaotic Systems ◽  
Auxiliary System ◽  
Generalized Synchronization ◽  
Ring Topology

The generalized synchronization of the complex network consisting of nodes being the chaotic systems via the auxiliary system approach is studied here. More specifically, the applicability of the auxiliary system approach to detect the generalized synchronization in the complex network consisting of unidirectional coupled chaotic systems in the cyclic chain is investigated. Such a complex network has the so-called ring topology. It is shown that the auxiliary system approach is useful for this purpose. The presented analysis is supported by the numerical simulations as well.

scholarly journals Synchronization in Tempered Fractional Complex Networks via Auxiliary System Approach

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Weiyuan Ma ◽  
Changpin Li ◽  
Jingwei Deng
Keyword(s):  
Fractional Derivative ◽  
Complex Networks ◽  
Waiting Time ◽  
System Approach ◽  
Physical Space ◽  
Pinning Control ◽  
Auxiliary System ◽  
Generalized Synchronization ◽  
Fractional Systems ◽  
First Moment

In the famous continuous time random walk (CTRW) model, because of the finite lifetime of biological particles, it is sometimes necessary to temper the power law measure such that the waiting time measure has a convergent first moment. The CTRW model with tempered waiting time measure is the so-called tempered fractional derivative. In this article, we introduce the tempered fractional derivative into complex networks to describe the finite life span or bounded physical space of nodes. Some properties of the tempered fractional derivative and tempered fractional systems are discussed. Generalized synchronization in two-layer tempered fractional complex networks via pinning control is addressed based on the auxiliary system approach. The results of the proposed theory are used to derive a sufficient condition for achieving generalized synchronization of tempered fractional networks. Numerical simulations are presented to illustrate the effectiveness of the methods.

Generalized synchronization of chaos: The auxiliary system approach

1996 ◽  
Vol 53 (5) ◽  
pp. 4528-4535 ◽  
Author(s):  
Henry D. I. Abarbanel ◽  
Nikolai F. Rulkov ◽  
Mikhail M. Sushchik
Keyword(s):  
System Approach ◽  
Auxiliary System ◽  
Generalized Synchronization

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.

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