scholarly journals Boundedness of the complex Chen system

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xu Zhang ◽  
Guanrong Chen
Keyword(s):  
Chen System

<p style='text-indent:20px;'>Some ultimate bounds are derived for the complex Chen system.</p>

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.

scholarly journals Study on Chaotic Fault Tolerant Synchronization Control Based on Adaptive Observer

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Dongming Chen ◽  
Xinyu Huang ◽  
Tao Ren
Keyword(s):  
Secure Communication ◽  
Chaotic Systems ◽  
Fault Tolerant ◽  
Sufficient Conditions ◽  
Adaptive Observer ◽  
Synchronization Control ◽  
Slave System ◽  
Chen System ◽  
Master System ◽  
Abrupt Faults

Aiming at the abrupt faults of the chaotic system, an adaptive observer is proposed to trace the states of the master system. The sufficient conditions for synchronization of such chaotic systems are also derived. Then the feasibility and effectiveness of the proposed method are illustrated via numerical simulations of chaotic Chen system. Finally, the proposed synchronization schemes are applied to secure communication system successfully. The experimental results demonstrate that the employed observer can manage real-time fault diagnosis and parameter identification as well as states tracing of the master system, and so the synchronization of master system and slave system is achieved.

scholarly journals Adaptive Projective Synchronization between Two Different Fractional-Order Chaotic Systems with Fully Unknown Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Liping Chen ◽  
Shanbi Wei ◽  
Yi Chai ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Unknown Parameters ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Response Systems ◽  
The Stability ◽  
Adaptive Control Law

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional-order chaotic Chen system and the fractional-order chaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

scholarly journals Adaptive tracking control of the Chen system

2007 ◽  
Vol 56 (10) ◽  
pp. 5661
Author(s):  
Chen Long ◽  
Wang De-Shi
Keyword(s):  
Tracking Control ◽  
Chen System ◽  
Adaptive Tracking Control ◽  
Adaptive Tracking

scholarly journals Chaos in the fractional-order conjugate Chen system and its circuit emulation

2009 ◽  
Vol 58 (5) ◽  
pp. 2957
Author(s):  
Zhang Ruo-Xun ◽  
Yang Shi-Ping
Keyword(s):  
Fractional Order ◽  
Chen System

Robust Control for Uncertain Unified Chaotic Systems with Input Nonlinearity via Improved Sliding Mode Technique

2011 ◽  
Vol 474-476 ◽  
pp. 2100-2105
Author(s):  
Xiao Jing Wu ◽  
Xue Li Wu
Keyword(s):  
Robust Control ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Lyapunov Theory ◽  
Chen System ◽  
Input Nonlinearity ◽  
Adaptive Parameter ◽  
Unified Chaotic Systems ◽  
Mode Technique ◽  
Sliding Mode Technique

This paper investigates the robust control problem of the uncertain unified chaotic systems subject to sector input nonlinearity. First, the adaptive parameter is introduced for designing sliding surface such that the parameters of the unified chaotic system are not necessary to know. Then, based on Lyapunov theory, the controller is designed via sliding mode technique, which cancels the assumption that the information on the bound of input nonlinearity should be known for designer in advance. Finally, the sliding mode controller is applied to ensure that different uncertain chaotic systems (Lorenz system, Lü system and Chen system) states can be regulated to zero levels asymptotically in the presence of sector input nonlinearity. The simulation results demonstrated the effectiveness of the proposed controller.

scholarly journals Application of Piecewise Successive Linearization Method for the Solutions of the Chen Chaotic System

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
S. S. Motsa ◽  
Y. Khan ◽  
S. Shateyi
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Good Accuracy ◽  
Linearization Method ◽  
Chen System ◽  
Successive Linearization Method ◽  
Runge Kutta

This paper centres on the application of the new piecewise successive linearization method (PSLM) in solving the chaotic and nonchaotic Chen system. Numerical simulations are presented graphically and comparison is made between the PSLM and Runge-Kutta-based methods. The work shows that the proposed method provides good accuracy and can be easily extended to other dynamical systems including those that are chaotic in nature.

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