Tracking the state of the delay hyperchaotic Lü system using the coullet chaotic system via a single controller

Complexity ◽  
2014 ◽  
Vol 21 (5) ◽  
pp. 125-130 ◽  
Author(s):  
Yan Zhou ◽  
Xuerong Shi ◽  
Zuolei Wang ◽  
Juanjuan Huang ◽  
Keming Tang ◽  
...  
Keyword(s):  
Chaotic System ◽  
The State ◽  
Lü System ◽  
Single Controller ◽  
Hyperchaotic Lu System ◽  
Lu System

ON THE BOUNDNESS OF SOME SOLUTIONS OF THE LÜ SYSTEM

2012 ◽  
Vol 22 (01) ◽  
pp. 1250015 ◽  
Author(s):  
FUCHEN ZHANG ◽  
CHUNLAI MU ◽  
XIAOWU LI
Keyword(s):  
Lyapunov Function ◽  
Chaotic System ◽  
System Parameters ◽  
Lü System ◽  
Lu System

By constructing a suitable Lyapunov function, we show that for the Lü chaotic system parameters in some specified regions, the solutions of the system are globally bounded.

scholarly journals Controlling Hopf Bifurcation of a New Modified Hyperchaotic Lü System

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Ping Cai ◽  
Jia-Shi Tang ◽  
Zhen-Bo Li
Keyword(s):  
Hopf Bifurcation ◽  
Control Strategy ◽  
State Feedback ◽  
Hybrid Control ◽  
Normal Form Theory ◽  
Lü System ◽  
Form Theory ◽  
Hyperchaotic Lu System ◽  
The Stability ◽  
Lu System

Controlling Hopf bifurcation of a new modified hyperchaotic Lü system is investigated in this paper. A hybrid control strategy using both state feedback and parameter control is proposed. The control strategy realizes the delay of Hopf bifurcation. Furthermore, by applying the normal form theory, the stability of the bifurcation is determined. Numerical simulation results are given to support the theoretical analysis.

Generating the New Chaotic Attractors of the Lorenz System Family via Anti-Controlling Method

2012 ◽  
Vol 542-543 ◽  
pp. 1042-1046 ◽  
Author(s):  
Xin Deng
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Attractors ◽  
Chen System ◽  
Lü System ◽  
New Chaotic System ◽  
Dynamical Properties ◽  
The Lorenz System ◽  
Lu System

In this paper, the first new chaotic system is gained by anti-controlling Chen system,which belongs to the general Lorenz system; also, the second new chaotic system is gained by anti-controlling the first new chaotic system, which belongs to the general Lü system. Moreover,some basic dynamical properties of two new chaotic systems are studied, either numerically or analytically. The obtained results show clearly that Chen chaotic system and two new chaotic systems also can form another Lorenz system family and deserve further detailed investigation.

Hybrid synchronization of hyperchaotic Lu system

Pramana ◽  
2009 ◽  
Vol 73 (4) ◽  
pp. 781-786 ◽  
Author(s):  
K. Sebastian Sudheer ◽  
M. Sabir
Keyword(s):  
Lü System ◽  
Hybrid Synchronization ◽  
Hyperchaotic Lu System ◽  
Lu System

IMPULSIVE SYNCHRONIZATION OF HYPERCHAOTIC LÜ SYSTEM

2011 ◽  
Vol 25 (27) ◽  
pp. 3671-3678 ◽  
Author(s):  
XING-YUAN WANG ◽  
MING-JUN WANG
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Impulsive Synchronization ◽  
Lü System ◽  
Feedback Strength ◽  
Hyperchaotic Lu System ◽  
Lu System

In this paper, the impulsive synchronization of hyperchaotic Lü systems is discussed. The sufficient conditions on feedback strength and impulsive interval are established to guarantee the synchronization. The method is proved true by Lyapunov stability theory. In addition, a scheme of impulsive synchronization via transmitting single signal is presented. Numerical simulations show the effectiveness of the methods.

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