scholarly journals A new method of synchronization between two different chaotic systems

2006 ◽  
Vol 55 (11) ◽  
pp. 5681
Author(s):  
Li Shuang ◽  
Xu Wei ◽  
Li Rui-Hong ◽  
Li Yu-Peng
Keyword(s):  
Chaotic Systems ◽  
New Method ◽  
Different Chaotic Systems

Chaos Anti-Synchronization between Chen System and Lu System

2014 ◽  
Vol 631-632 ◽  
pp. 710-713 ◽  
Author(s):  
Xian Yong Wu ◽  
Hao Wu ◽  
Hao Gong
Keyword(s):  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Theory ◽  
State Variables ◽  
Chen System ◽  
System Parameters ◽  
Control Scheme ◽  
Error Dynamics ◽  
The Stability ◽  
Different Chaotic Systems

Anti-synchronization of two different chaotic systems is investigated. On the basis of Lyapunov theory, adaptive control scheme is proposed when system parameters are unknown, sufficient conditions for the stability of the error dynamics are derived, where the controllers are designed using the sum of the state variables in chaotic systems. Numerical simulations are performed for the Chen and Lu systems to demonstrate the effectiveness of the proposed control strategy.

Deep Learning Based Classification of Time Series of Chaotic Systems over Graphic Images

2021 ◽  
Author(s):  
Süleyman UZUN ◽  
Sezgin KAÇAR ◽  
Burak ARICIOĞLU
Keyword(s):  
Time Series ◽  
Deep Learning ◽  
Transfer Learning ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Step Size ◽  
Learning Methods ◽  
Data Set ◽  
Graphic Images ◽  
Different Chaotic Systems

Abstract In this study, for the first time in the literature, identification of different chaotic systems by classifying graphic images of their time series with deep learning methods is aimed. For this purpose, a data set is generated that consists of the graphic images of time series of the most known three chaotic systems: Lorenz, Chen, and Rossler systems. The time series are obtained for different parameter values, initial conditions, step size and time lengths. After generating the data set, a high-accuracy classification is performed by using transfer learning method. In the study, the most accepted deep learning models of the transfer learning methods are employed. These models are SqueezeNet, VGG-19, AlexNet, ResNet50, ResNet101, DenseNet201, ShuffleNet and GoogLeNet. As a result of the study, classification accuracy is found between 96% and 97% depending on the problem. Thus, this study makes association of real time random signals with a mathematical system possible.

THE HYBRID FUNCTION PROJECTIVE SYNCHRONIZATION OF CHAOTIC SYSTEMS

2009 ◽  
Vol 20 (05) ◽  
pp. 789-797
Author(s):  
YONG-GUANG YU ◽  
HAN-XIONG LI ◽  
JUN-ZHI YU
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Function Projective Synchronization ◽  
Hybrid Function ◽  
Simulation Results ◽  
Different Chaotic Systems

This paper mainly investigated a hybrid function projective synchronization of two different chaotic systems. Based on the Lyapunov stability theory, an adaptive controller for the synchronization of two different chaotic systems is designed. This technique is applied to achieve the synchronization between Lorenz and Rössler chaotic systems, and the synchronization of hyperchaotic Rössler and Chen systems. The numerical simulation results illustrate the effectiveness and feasibility of the proposed scheme.

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