Global finite-time chaos synchronization between the Loren system and the Chen system via a simple controller

2020 ◽  
Author(s):  
CHEN Yun ◽  
ZHOU Dawei ◽  
LI Shilei ◽  
ZHANG Xiyong
Keyword(s):  
Finite Time ◽  
Chaos Synchronization ◽  
Chen System

scholarly journals Analysis of a Lorenz-Like Chaotic System by Lyapunov Functions

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Fuchen Zhang
Keyword(s):  
Chaotic System ◽  
Chaos Synchronization ◽  
Lorenz System ◽  
Chen System ◽  
Lyapunov Function Method ◽  
Exponential Attractivity ◽  
Positively Invariant Set ◽  
Ultimate Bound ◽  
Special Case ◽  
Theoretical Results

In this paper, we investigate the ultimate bound set and positively invariant set of a 3D Lorenz-like chaotic system, which is different from the well-known Lorenz system, Rössler system, Chen system, Lü system, and even Lorenz system family. Furthermore, we investigate the global exponential attractive set of this system via the Lyapunov function method. The rate of the trajectories going from the exterior of the globally exponential attractive set to the interior of the globally exponential attractive set is also obtained for all the positive parameters values a,b,c. The innovation of this paper is that our approach to construct the ultimate bounded and globally exponential attractivity sets assumes that the corresponding sets depend on some artificial parameters (λ and m); that is, for the fixed parameters of the system, we have a series of sets depending on λ and m. The results contain the known result as a special case for the fixed λ and m. The efficiency of the scheme is shown numerically. The theoretical results may find wide applications in chaos control and chaos synchronization.

Robust finite-time chaos synchronization of time-delay chaotic systems and its application in secure communication

2016 ◽  
Vol 40 (4) ◽  
pp. 1177-1187 ◽  
Author(s):  
Hua Wang ◽  
Jian-Min Ye ◽  
Zhong–Hua Miao ◽  
Edmond A Jonckheere
Keyword(s):  
Time Delay ◽  
Numerical Simulations ◽  
Finite Time ◽  
Secure Communication ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Chaotic Synchronization ◽  
Uncertain Parameters ◽  
Wide Range ◽  
Zero Items

This paper presents finite-time chaos synchronization of time-delay chaotic systems with uncertain parameters. According to the proposed method, a lot of coupled items can be treated as zero items. Thus, the whole system can be simplified greatly. Based on robust chaotic synchronization, secure communication can be realized with a wide range of parameter disturbance and time-delay. Numerical simulations are provided to illustrate the effectiveness of the proposed method.

Adaptive Projective Synchronization of the New Three-Dimensional Chaotic System

2013 ◽  
Vol 321-324 ◽  
pp. 921-924 ◽  
Author(s):  
Su Hai Huang
Keyword(s):  
Chaotic System ◽  
Finite Time ◽  
Chaos Synchronization ◽  
Three Dimensional ◽  
Projective Synchronization ◽  
Time Stability ◽  
Finite Time Stability ◽  
Adaptive Technique ◽  
New Chaotic System ◽  
Synchronization Scheme

This paper deals with the finite-time chaos synchronization of the new chaotic system [with uncertain parameters. Based on the finite-time stability theory and adaptive technique, a controller has been designed to realize finite-time chaos projective synchronization and parameter identification. Moreover, numerical simulation result is included to demonstrate the effectiveness and feasibility of the proposed synchronization scheme.

Chaos synchronization between Chen system and Genesio system

2007 ◽  
Vol 364 (6) ◽  
pp. 484-487 ◽  
Author(s):  
Xianyong Wu ◽  
Zhi-Hong Guan ◽  
Zhengping Wu ◽  
Tao Li
Keyword(s):  
Chaos Synchronization ◽  
Chen System

Finite-time chaos synchronization and its application in wireless sensor networks

2017 ◽  
Vol 40 (13) ◽  
pp. 3788-3799 ◽  
Author(s):  
Behrouz Vaseghi ◽  
Mohammad Ali Pourmina ◽  
Saleh Mobayen
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Finite Time ◽  
Secure Communication ◽  
Chaos Synchronization ◽  
Sliding Mode ◽  
Base Station ◽  
Sensor Nodes ◽  
Wireless Sensor ◽  
Control Law

This paper considers the finite-time chaos synchronization of Chua chaotic oscillators based on the secure communication scheme in wireless sensor networks. The modified Chua oscillators are added to the base station and sensor nodes to generate the chaotic signals. Two methods are proposed for the finite-time synchronization of the modified Chua systems with uncertain parameters. In the first method, by using the Lyapunov stability theory, control law is suggested to achieve finite-time chaos synchronization. In order to increase the robustness of the controller, in the second method, a sliding mode controller is applied to the wireless sensor network. Synchronization between the base station and each of the sensor nodes is realized by multiplying a selection matrix by the specified chaotic signal, which is broadcasted by the base station to the sensor nodes. The mathematical proofs confirm that the proposed control law is correct and finally, the simulation results are presented to show the efficiency of the proposed technique.

INITIAL RECTIFIED ATTRACTORS FOR PERFECT GS AND Q-S SYNCHRONIZATION OF CHAOTIC SYSTEMS

2011 ◽  
Vol 25 (06) ◽  
pp. 863-876
Author(s):  
SMAIL ALIBEAKI ◽  
MOHAMMAD HAERI ◽  
MOHAMMAD SALEH TAVAZOEI
Keyword(s):  
Finite Time ◽  
Numerical Experiments ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Time Interval ◽  
Finite Time Interval ◽  
Response Systems

The controlled attractor with initial rectifying action, referred to as initial rectified attractor (IRA) in this paper, is introduced for the purpose of generalized and Q-S chaos synchronization. The IRA is designed to make the states of drive and response systems synchronized in the form of generalized and Q-S within a finite time interval. The reaching time is shown to be independent of the initial conditions and dynamics of the chaotic systems, and can be determined in advance. With numerical experiments it is demonstrated that perfect synchronization can be achieved between the modified Lorenz and the hyperchaotic Rössler systems in different configurations.

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