Global synchronization of two parametrically excited systems using active control

2006 ◽  
Vol 28 (2) ◽  
pp. 428-436 ◽  
Author(s):  
Youming Lei ◽  
Wei Xu ◽  
Jianwei Shen ◽  
Tong Fang
Keyword(s):  
Active Control ◽  
Global Synchronization ◽  
Parametrically Excited

Global synchronization of two Ghostburster neurons via active control

2009 ◽  
Vol 40 (3) ◽  
pp. 1213-1220 ◽  
Author(s):  
Li Sun ◽  
Jiang Wang ◽  
Bin Deng
Keyword(s):  
Active Control ◽  
Global Synchronization

A TYPE OF SINGLE SCROLL ATTRACTOR CHAOS SYNCHRONIZATION

2010 ◽  
Vol 24 (27) ◽  
pp. 5269-5283
Author(s):  
TIANSHU WANG ◽  
XINGYUAN WANG
Keyword(s):  
Numerical Simulations ◽  
Active Control ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Function ◽  
Function Parameter ◽  
Nonlinear Feedback ◽  
Global Synchronization ◽  
Linear And Nonlinear ◽  
Different Chaotic Systems

This paper studies a type of single scroll attractor chaos system. Based on the research of Jiang et al. the global synchronization method is designed, and moreover, the author uses a combined synchronization of linear and nonlinear feedback, active control, single vector and unidirectional coupling synchronization three methods else, the problem of synchronization between same and different chaotic systems are realized by the four methods, respectively. The range of control function parameter is discussed according to the Routh–Hurwitz criterion and numerical simulations show the effectiveness of them.

scholarly journals On nonlinear dynamics of a parametrically excited pendulum using both active control and passive rotational (MR) damper

2017 ◽  
Vol 24 (9) ◽  
pp. 1587-1599 ◽  
Author(s):  
AM Tusset ◽  
FC Janzen ◽  
V Piccirillo ◽  
RT Rocha ◽  
JM Balthazar ◽  
...  
Keyword(s):  
Active Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Mr Damper ◽  
The Other ◽  
Parametric Uncertainties ◽  
Nonlinear Saturation ◽  
Saturation Control ◽  
Parametrically Excited ◽  
Pendulum Oscillation

This paper presents two control strategies for a parametrically excited pendulum with chaotic behavior. One of them considers active control obtained by nonlinear saturation control (NSC) and the other a passive rotational magnetorheological (MR) damper. Firstly, the active control problem was formulated in order to design the external torque for the pendulum, considering the NSC. Numerical simulations were carried out in order to show the effectiveness of this method for the active control of the pendulum oscillation. The ability of the control of the proposed NSC in suppression of the chaotic behavior, considering the proposed parameters, was tested by a sensitivity analysis to parametric uncertainties. In the case of the passive rotational MR damper, firstly the influence of the introduction of the MR in a pendulum was performed considering the 0-1 test. Different electric currents are applied to suppress the chaotic behavior of the system. The numerical results showed that the simple introduction of a passive rotational MR damper without electric current did not change the chaotic behavior of the system. However, it is possible to keep the pendulum oscillating with periodic behavior using the rotational MR damper with energizing discontinuity.

Synchronization of Hyperchaotic Memristor-Based Chua’s Circuits

2014 ◽  
Vol 644-650 ◽  
pp. 3485-3488
Author(s):  
Hai Long Huang ◽  
Yan Peng ◽  
Jun Jian Huang
Keyword(s):  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Sufficient Condition ◽  
Global Synchronization ◽  
Error System ◽  
The Stability ◽  
Active Control Method

This paper further investigates the problem of synchronization of hyperchaotic memristor-based Chua’s circuits. An active control method is employed to design a controller to achieve the global synchronization of two identical memristor-based systems. Based on Lyapunov stability theory, a sufficient condition is given to guarantee the stability of the synchronization error system.

ACTIVE CONTROL AND GLOBAL SYNCHRONIZATION OF THE COMPLEX CHEN AND LÜ SYSTEMS

2007 ◽  
Vol 17 (12) ◽  
pp. 4295-4308 ◽  
Author(s):  
GAMAL M. MAHMOUD ◽  
TASSOS BOUNTIS ◽  
EMAD E. MAHMOUD
Keyword(s):  
Dynamical Systems ◽  
Active Control ◽  
Chaos Synchronization ◽  
Function Analysis ◽  
Nonlinear Phenomenon ◽  
Global Synchronization ◽  
The Lorenz System ◽  
The Stability ◽  
Liquid Flows ◽  
Drive And Control

Chaos synchronization is a very important nonlinear phenomenon, which has been studied to date extensively on dynamical systems described by real variables. There also exist, however, interesting cases of dynamical systems, where the main variables participating in the dynamics are complex, for example, when amplitudes of electromagnetic fields are involved. Another example is when chaos synchronization is used for communications, where doubling the number of variables may be used to increase the content and security of the transmitted information. It is also well-known that similar generalization of the Lorenz system to one with complex ODEs has been introduced to describe and simulate the physics of a detuned laser and thermal convection of liquid flows. In this paper, we study chaos synchronization by applying active control and Lyapunov function analysis to two such systems introduced by Chen and Lü. First we show that, written in terms of complex variables, these systems can have chaotic dynamics and exhibit strange attractors. We calculate numerically the values of the parameters at which these attractors exist. Active control and global synchronization techniques are then applied to study the phenomenon of chaos synchronization. Analytical criteria concerning the stability of these techniques are implemented and excellent agreement is found upon comparison with numerical experiments. In particular, studying the time evolution of "errors" (or differences between drive and control dynamics), we show that both techniques are very effective for controlling the behavior of these systems, even in regimes of very strong chaos.

Sign in / Sign up

Export Citation Format

Share Document