Research of Generalized Lorenz System Family and Chua's Circuit Based on Simulink

1999 ◽  
Vol 09 (07) ◽  
pp. 1425-1434 ◽  
Author(s):  
SAVERIO MASCOLO ◽  
GIUSEPPE GRASSI

In this Letter backstepping design is proposed for controlling chaotic systems. The tool consists in a recursive procedure that combines the choice of a Lyapunov function with the design of feedback control. The advantages of the method are the following: (i) it represents a systematic procedure for controlling chaotic or hyperchaotic dynamics; (ii) it can be applied to several circuits and systems reported in literature; (iii) stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory can be achieved. In order to illustrate the general applicability of backstepping design, the tool is utilized for controlling the chaotic dynamics of the Lorenz system and Chua's circuit. Finally, numerical simulations are carried out to show the effectiveness of the technique.


2004 ◽  
Vol 14 (09) ◽  
pp. 3277-3293 ◽  
Author(s):  
RECAI KILIÇ ◽  
MUSTAFA ALÇI ◽  
ENIS GÜNAY

The impulsive synchronization method has been applied to several well-known chaotic circuits and systems such as Chua's circuit, Lorenz system and hyperchaotic circuit in the literature. In this paper, we also present two impulsive synchronization studies using SC-CNN-based circuit and Chua's circuit. In the first study, we have investigated the impulsive synchronization between two SC-CNN-based circuits. Pspice simulation results show that two SC-CNN-based circuits can be synchronized impulsively via x1 and x2 cell dynamics for different impulse width and impulse period values. And in the second study, we have investigated the impulsive synchronization between SC-CNN-based circuit and Chua's circuit. Pspice simulation results verify that two chaotic circuits, which have identical dynamical systems via appropriate parameter transformations but having quite different hardware implementations, can be synchronized impulsively for different impulse width and impulse period values.


2005 ◽  
Vol 14 (02) ◽  
pp. 333-346 ◽  
Author(s):  
RECAİ KILIÇ

So far, impulsive synchronization method has been applied to several well-known chaotic circuits and systems such as Chua's circuit, Lorenz system and hyperchaotic circuit. Here, we present a study of impulsive synchronization of another chaotic circuit, namely mixed-mode chaotic circuit which oscillates both autonomous and nonautonomous chaotic dynamics. By choosing two mixed-mode chaotic circuits as driving and driven chaotic circuits, we investigated whether these circuits are synchronized impulsively or not by evaluating the minimum length of impulse width (Q), and the ratio of impulse width to impulse period (Q/T). The results of our investigation confirm that two mixed-mode chaotic circuits can be synchronized impulsively with very narrow impulse width.


1993 ◽  
Vol 03 (02) ◽  
pp. 645-668 ◽  
Author(s):  
A. N. SHARKOVSKY ◽  
YU. MAISTRENKO ◽  
PH. DEREGEL ◽  
L. O. CHUA

In this paper, we consider an infinite-dimensional extension of Chua's circuit (Fig. 1) obtained by replacing the left portion of the circuit composed of the capacitance C2 and the inductance L by a lossless transmission line as shown in Fig. 2. As we shall see, if the remaining capacitance C1 is equal to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced to that of a scalar nonlinear difference equation. After deriving the corresponding 1-D map, it will be possible to determine without any approximation the analytical equation of the stability boundaries of cycles of every period n. Since the stability region is nonempty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.


Sign in / Sign up

Export Citation Format

Share Document