Controlling the Chaotic n-Scroll Chua's Circuit

2003 ◽  
Vol 13 (09) ◽  
pp. 2709-2714 ◽  
Author(s):  
Yan-Li Zou ◽  
Xiao-Shu Luo ◽  
Pin-Qun Jiang ◽  
Bing-Hong Wang ◽  
Guanrong Chen ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Fixed Points ◽  
Chaos Control ◽  
Control Method ◽  
Chua’S Circuit ◽  
System Matrix ◽  
Chua's Circuit ◽  
State Variable ◽  
Different Types ◽  
Linearized System

In this paper, controlling chaos in the chaotic n-scroll Chua's circuit is studied. The approach taken is to use feedback of a single state variable in a simple PD (proportional and differential) format. First, the unstable fixed points in the n-scroll Chua's circuit are classified into two different types according to the characteristics of the eigenvalues of the linearized system matrix at the fixed points. Then, the controllability of these two-types of fixed points is studied. Theoretical analysis shows that the first type of unstable fixed points can be stabilized, at which Hopf bifurcation can also be generated. Control results of the n-scroll Chua's circuit are then demonstrated. Both theoretical analysis and numerical simulation results show that the proposed chaos control method is indeed effective.

EXPERIMENTAL VERIFICATION OF PYRAGAS’S CHAOS CONTROL METHOD APPLIED TO CHUA’S CIRCUIT

1994 ◽  
Vol 04 (06) ◽  
pp. 1703-1706 ◽  
Author(s):  
P. CELKA
Keyword(s):  
Periodic Orbits ◽  
Experimental Verification ◽  
Chaos Control ◽  
Control Method ◽  
Experimental Results ◽  
Experimental Setup ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit

We have built an experimental setup to apply Pyragas’s [1992, 1993] control method in order to stabilize unstable periodic orbits (UPO) in Chua’s circuit. We have been able to control low period UPO embedded in the double scroll attractor. However, experimental results show that the control method is useful under some restrictions we will discuss.

CONTROL OF n-SCROLL CHUA'S CIRCUIT

2009 ◽  
Vol 19 (11) ◽  
pp. 3813-3822 ◽  
Author(s):  
ABDELKRIM BOUKABOU ◽  
BILEL SAYOUD ◽  
HAMZA BOUMAIZA ◽  
NOURA MANSOURI
Keyword(s):  
Numerical Simulations ◽  
Fixed Points ◽  
Periodic Orbits ◽  
Predictive Control ◽  
Control Method ◽  
Sufficient Conditions ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit ◽  
Necessary And Sufficient

This paper addresses the control of unstable fixed points and unstable periodic orbits of the n-scroll Chua's circuit. In a first step, we give necessary and sufficient conditions for exponential stabilization of unstable fixed points by the proposed predictive control method. In addition, we show how a chaotic system with multiple unstable periodic orbits can be stabilized by taking the system dynamics from one UPO to another. Control performances of these approaches are demonstrated by numerical simulations.

PERIODIC RESPONSE TO EXTERNAL STIMULATION OF A CHAOTIC NEURAL NETWORK WITH DELAYED FEEDBACK

1999 ◽  
Vol 09 (04) ◽  
pp. 713-722 ◽  
Author(s):  
ALBAN PUI MAN TSUI ◽  
ANTONIA J. JONES
Keyword(s):  
Neural Network ◽  
Chaos Control ◽  
Control Method ◽  
Original System ◽  
Neural System ◽  
Delayed Feedback ◽  
Input Stimulus ◽  
Biologically Inspired ◽  
External Stimulation ◽  
Different Types

We construct a feedforward neural network so that when the outputs are fed back into the inputs and the system is iterated it behaves chaotically. We call this the "rest state". Suppose now that an input stimulus is added to one or more inputs. Following a biologically inspired model suggested by Freeman [1991], under these conditions we should want the behavior of the network to stabilize into an unstable periodic orbit of the original system. We call this the "retrieval behavior" since it is analogous to the act of recognition. Standard methods of chaos control, such as OGY for example, used to elicit the retrieval behavior would be inappropriate, since such methods involve calculations external to the system being controlled and can be considered unlikely in a biological neural network. Using a chaos control method originally suggested by Pyragas [1992] we show that retrieval behavior can occur as a result of delayed feedback and examine the variety of the responses that arise under different types of stimuli and under noise. This artificial neural system has a strong dynamical parallel to Freeman's observed biological phenomenon.

scholarly journals Adaptive Control of Chaos in Chua's Circuit

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Weiping Guo ◽  
Diantong Liu
Keyword(s):  
Feedback Control ◽  
Control Method ◽  
Equilibrium Points ◽  
Lyapunov Theory ◽  
Chua’S Circuit ◽  
Control Of Chaos ◽  
Chua's Circuit ◽  
Adaptive Technology ◽  
Feedback Control Method ◽  
And Control

A feedback control method and an adaptive feedback control method are proposed for Chua's circuit chaos system, which is a simple 3D autonomous system. The asymptotical stability is proven with Lyapunov theory for both of the proposed methods, and the system can be dragged to one of its three unstable equilibrium points respectively. Simulation results show that the proposed methods are valid, and control performance is improved through introducing adaptive technology.

ADAPTIVE CONTROL OF CHAOTIC n-SCROLL CHUA'S CIRCUIT

2006 ◽  
Vol 16 (04) ◽  
pp. 1089-1096 ◽  
Author(s):  
YAN-LI ZOU ◽  
JIE ZHU ◽  
GUANRONG CHEN
Keyword(s):  
Adaptive Control ◽  
Control Method ◽  
Control Methods ◽  
Chua’S Circuit ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Chua's Circuit ◽  
Low Pass ◽  
Attraction Basins ◽  
And Performance

In this paper, stabilization of fixed points of n-scroll Chua's circuit is investigated. Two adaptive control methods are proposed. One is based on an unstable low pass filter; the other is based on a stable and an unstable low pass filter. The simulation results verify the effectiveness of the two proposed control methods and performance comparisons show that the second control method is superior to the first one with regard to control speed and attraction basins.

HYPERCHAOS IN A CHUA'S CIRCUIT WITH TWO NEW ADDED BRANCHES

2008 ◽  
Vol 18 (04) ◽  
pp. 1151-1159 ◽  
Author(s):  
RUY BARBOZA
Keyword(s):  
Theoretical Analysis ◽  
Fourth Order ◽  
Current Source ◽  
Experimental Results ◽  
The Other ◽  
Chua’S Circuit ◽  
Series Connection ◽  
Chua's Circuit ◽  
Original Topology ◽  
Wide Range

In this work a fourth-order Chua's circuit, capable of generating hyperchaotic oscillations in a wide range of parameters, is presented. The circuit is obtained by adding two new branches to the original topology of the Chua's double scroll circuit. One of the added branches is a linear inductor-resistor series connection, and the other one is a nonlinear voltage-controlled current source. A theoretical analysis of the circuit equations is presented, along with numerical and experimental results.

scholarly journals ORDERING CHAOS IN CHUA'S CIRCUIT: A SAMPLED-DATA FEEDBACK AND DIGITAL REDESIGN APPROACH

2000 ◽  
Vol 10 (09) ◽  
pp. 2221-2231 ◽  
Author(s):  
SHU-MEI GUO ◽  
LEANG S. SHIEH ◽  
GUANRONG CHEN ◽  
MARITZA ORTEGA
Keyword(s):  
Control Method ◽  
Digital Design ◽  
Chua’S Circuit ◽  
Sampled Data ◽  
Nonlinear Circuit ◽  
Chua's Circuit ◽  
Digital Redesign ◽  
Data Feedback ◽  
Feedback Control Method ◽  
Sampling Times

In this paper, we develop and apply some digital design and redesign techniques for ordering the chaotic Chua's circuit. The idea of using sampled-data feedback for controlling the circuit was previously suggested [Yang & Chua, 1998], which relies on small sampling periods. We show how this sampled-data feedback control method can be significantly improved, so that large sampling times are allowed, for the same purpose of ordering the nonlinear circuit, from anywhere within the chaotic attractor towards a predesired periodic cycle of the circuit.

GENERATION OF n × m-SCROLL ATTRACTORS UNDER A CHUA-CIRCUIT FRAMEWORK

2007 ◽  
Vol 17 (11) ◽  
pp. 3951-3964 ◽  
Author(s):  
SIMIN YU ◽  
WALLACE K. S. TANG ◽  
G. CHEN
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Chua’S Circuit ◽  
Electronic Circuits ◽  
Third Order ◽  
Chua's Circuit ◽  
Chua Circuit ◽  
Dynamical Behaviors ◽  
First Time

In this paper, the generation of n × m-scroll attractors under a Chua-circuit framework is presented. By using a sawtooth function, f1(x), and a staircase function, f2(y), n × m-scroll attractors can be generated and observed from a third-order circuit. Its dynamical behaviors are investigated by means of theoretical analysis as well as numerical simulation. Moreover, two electronic circuits are designed for its realization, and experimental observations of n × m-scroll attractors based on Chua's circuit are reported, for the first time in the literature.

scholarly journals Chaos and Control of Game Model Based on Heterogeneous Expectations in Electric Power Triopoly

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Weizhuo Ji
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Electric Power ◽  
Chaos Control ◽  
Control Method ◽  
Repeated Game ◽  
Game Model ◽  
Heterogeneous Expectations ◽  
Straight Line ◽  
And Control

A dynamic repeated game model has been established based on heterogeneous expectations in electric power triopoly. Theoretical analysis and numerical simulation show the complexity of this model; suppose that the producers make decisions with naive expectation and bounded rationality. The straight-line stabilization chaos control method was successfully applied to the dynamic repeated game model. The results have important practical value for the producers in the electric power oligopoly.

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