scholarly journals Controlling Chaotic Systems via Time-delayed Control

2021 ◽  
Vol 15 ◽  
pp. 44-49
Author(s):  
Ramy Farid ◽  
Abdul-Azim Ibrahim ◽  
Belal Abou-Zalam
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Unstable Equilibrium ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Integral Time ◽  
Lyapunov Stabilization

Based on Lyapunov stabilization theory, this paper proposes a proportional plus integral time-delayed controller to stabilize unstable equilibrium points (UPOs) embedded in chaotic attractors. The criterion is successfully applied to the classic Chua's circuit. Theoretical analysis and numerical simulation show the effectiveness of this controller.

Design of Grid Multiscroll Chaotic Attractors via Transformations

2015 ◽  
Vol 25 (10) ◽  
pp. 1530027 ◽  
Author(s):  
Xingxing Ai ◽  
Kehui Sun ◽  
Shaobo He ◽  
Huihai Wang
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponent ◽  
Theoretical Analysis ◽  
Experimental Verification ◽  
Equilibrium Points ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
Largest Lyapunov Exponent ◽  
One Dimensional ◽  
Circular Grid

Three transformation approaches for generating grid multiscroll chaotic attractors are presented through theoretical analysis and numerical simulation. Three kinds of grid multiscroll chaotic attractors are generated based on one-dimensional multiscroll Chua system. The dynamics of the multiscroll chaotic attractors are analyzed by means of equilibrium points, eigenvalues, the largest Lyapunov exponent and complexity. As the experimental verification, we implemented the circular grid multiscroll attractor on DSP platform. The simulation and experimental results are consistent well with that of theoretical analysis, and it shows that the design approaches are effective.

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.

Coexistence of Multiple Attractors in an Active Diode Pair Based Chua’s Circuit

2018 ◽  
Vol 28 (02) ◽  
pp. 1850019 ◽  
Author(s):  
Bocheng Bao ◽  
Huagan Wu ◽  
Li Xu ◽  
Mo Chen ◽  
Wen Hu
Keyword(s):  
Equilibrium Points ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Multiple Attractors ◽  
Stable Point ◽  
Chua's Circuit ◽  
Coexistence Of Multiple Attractors ◽  
Dynamical Properties ◽  
Nonzero Equilibrium ◽  
Made In

This paper focuses on the coexistence of multiple attractors in an active diode pair based Chua’s circuit with smooth nonlinearity. With dimensionless equations, dynamical properties, including boundness of system orbits and stability distributions of two nonzero equilibrium points, are investigated, and complex coexisting behaviors of multiple kinds of disconnected attractors of stable point attractors, limit cycles and chaotic attractors are numerically revealed. The results show that unlike the classical Chua’s circuit, the proposed circuit has two stable nonzero node-foci for the specified circuit parameters, thereby resulting in the emergence of multistability phenomenon. Based on two general impedance converters, the active diode pair based Chua’s circuit with an adjustable inductor and an adjustable capacitor is made in hardware, from which coexisting multiple attractors are conveniently captured.

GLOBAL ANALYSIS ON n-SCROLL CHAOTIC ATTRACTORS OF MODIFIED CHUA'S CIRCUIT

2009 ◽  
Vol 19 (01) ◽  
pp. 135-157 ◽  
Author(s):  
FEI XU ◽  
PEI YU ◽  
XIAOXIN LIAO
Keyword(s):  
Feedback Control ◽  
Global Analysis ◽  
Equilibrium Points ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Nonlinear Feedback ◽  
Control Laws ◽  
Chua's Circuit ◽  
Constructive Feedback ◽  
Globally Attractive

In this paper, we present a further mathematical study on the report of existence of n-scroll chaotic attractors in a modified Chua's circuit. A series of results based on mathematical theory are given. First, we show that the chaotic attractors of the modified Chua's circuit are globally attractive, with estimations given for the globally attractive set and positive invariant set. Then, we study the positions, number and local stability of the equilibrium points. We also design simple feedback control laws to globally exponentially stabilize any given equilibrium point. Finally, we use the theory and methodology of absolute stability of Luré nonlinear control systems and nonlinear feedback control to exponentially synchronize two modified Chua's circuits with the same structure. The design of constructive feedback control laws for synchronization is also discussed.

scholarly journals A GLOBAL SYNCHRONIZATION CRITERION FOR COUPLED CHAOTIC SYSTEMS VIA UNIDIRECTIONAL LINEAR ERROR FEEDBACK APPROACH

2002 ◽  
Vol 12 (10) ◽  
pp. 2239-2253 ◽  
Author(s):  
GUO-PING JIANG ◽  
WALLACE K. S. TANG
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Coupled Systems ◽  
Chua’S Circuit ◽  
Error Feedback ◽  
Chua's Circuit ◽  
Lyapunov Stabilization ◽  
Coupling Parameters ◽  
Coupling Approach ◽  
New Criterion

Based on Lyapunov stabilization theory, this paper proposes a new generic criterion of global chaos synchronization between two coupled chaotic systems from a unidirectional linear error feedback coupling approach. The criterion is successfully applied to some typical chaotic systems with different types of nonlinearity, such as the classic Chua's circuit, the modified Chua's circuit with a sine function, and the Rössler and Lorenz chaotic systems. The coupling parameters are determined according to the new criterion so as to ensure the coupled systems' global chaos synchronization.

Design of High-Order Chaotic Circuits

2013 ◽  
Vol 722 ◽  
pp. 33-43
Author(s):  
Zi Long Tang ◽  
Si Min Yu
Keyword(s):  
Equilibrium Points ◽  
Digital Processing ◽  
Negative Resistance ◽  
State Equation ◽  
High Order ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Dimensionless Equation ◽  
Seventh Order

As an expansion and extension for three-order and four-order Chua's circuit, a new method to construct a class of high-order Chua's circuit and its FPGA hardware implementation has been studied in this paper. Based on the structure of a typical third-order Chua's circuit, a fifth-order, sixth-order and seventh-order Chua's circuit have been constructed through the series in the-type sub-circuit made up by a negative resistance, capacitance, inductance, and resistance, which are stringed into on the inductance slip. The dimensionless equation of high-order Chua's circuit has been, then, derived, and its basic dynamics characteristics have also been analyzed, among which including the phase diagram of chaotic attractors, the dynamic behavior of equilibrium points, bifurcation diagram and the Lyapnuov exponents. Due to digital processing technology, the continuous time state equation of the system has been discretizationed and the state variable ratio transformation has been done, so that the chaotic attractors of high-order Chua's circuit can be generated by using FPGA technology. Taking seventh-order Chua's circuit as a typical example, a general design principle by the way of FPGA technology to generate chaotic attractors as well as the corresponding hardware realization has been presented.

Stability Analysis and Mapping of Multiple Dynamics of Chua’s Circuit in Full Four-Parameter Spaces

2015 ◽  
Vol 25 (13) ◽  
pp. 1530037 ◽  
Author(s):  
Ronilson Rocha ◽  
Rene Orlando Medrano-T.
Keyword(s):  
Stability Analysis ◽  
Theoretical Analysis ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Chua’S Circuit ◽  
Parameter Spaces ◽  
Chua's Circuit ◽  
Describing Functions ◽  
Route To Chaos ◽  
The Stability

The stability analysis is used in order to identify and to map different dynamics of Chua’s circuit in full four-parameter spaces. The study is performed using describing functions that allow to identify fixed point, periodic orbit, and unstable states with relative accuracy, as well as to predict route to chaos and hidden dynamics that conventional computational methods do not detect. Numerical investigations based on the computation of eigenvalues and Lyapunov exponents partially support the predictions obtained from the theoretical analysis since they do not capture the multiple dynamics that can coexist in the operation of Chua’s circuit. Attractors obtained from initial conditions outside of neighborhoods of the equilibrium points confirm the multiplicity of dynamics in the operation of Chua’s circuit and corroborate the theoretical analysis.

STOCHASTIC RESONANCE IN CHUA’S CIRCUIT DRIVEN BY AMPLITUDE OR FREQUENCY MODULATED SIGNALS

1994 ◽  
Vol 04 (02) ◽  
pp. 441-446 ◽  
Author(s):  
V.S. ANISHCHENKO ◽  
M.A. SAFONOVA ◽  
L.O. CHUA
Keyword(s):  
Numerical Simulation ◽  
Stochastic Resonance ◽  
Signal To Noise Ratio ◽  
Point Of View ◽  
Chua’S Circuit ◽  
Signal Distortion ◽  
Signal To Noise ◽  
Chua's Circuit ◽  
Noise Ratio ◽  
Modulated Signals

Using numerical simulation, we establish the possibility of realizing the stochastic resonance (SR) phenomenon in Chua’s circuit when it is excited by either an amplitude-modulated or a frequency-modulated signal. It is shown that the application of a frequency-modulated signal to a Chua’s circuit operating in a regime of dynamical intermittency is preferable over an amplitude-modulated signal from the point of view of minimizing the signal distortion and maximizing the signal-to-noise ratio (SNR).

scholarly journals A Novel 2D – Grid of Scroll Chaotic Attractor Generated by CNN

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 99 ◽  
Author(s):  
Ahmed M. Ali ◽  
Saif M. Ramadhan ◽  
Fadhil R. Tahir
Keyword(s):  
Theoretical Analysis ◽  
Chaotic Attractor ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Chaotic Attractors ◽  
Electronic Circuits ◽  
Nonlinear Networks ◽  
Design And Implementation ◽  
Simulation Results ◽  
New System

The complex grid of scroll chaotic attractors that are generated through nonlinear electronic circuits have been raised considerably over the last decades. In this paper, it is shown that a subclass of Cellular Nonlinear Networks (CNNs) allows us to generate complex dynamics and chaos in symmetry pattern. A novel grid of scroll chaotic attractor, based on a new system, shows symmetry scrolls about the origin. Also, the equilibrium points are located in a manner such that the symmetry about the line x=y has been achieved. The complex dynamics of system can be generated using CNNs, which in turn are derived from a CNN array (1×3) cells. The paper concerns on the design and implementation of 2×2 and 3×3 2D-grid of scroll via the CNN model. Theoretical analysis and numerical simulations of the derived model are included. The simulation results reveal that the grid of scroll attractors can be successfully reproduced using PSpice.

CHAOTIC BEHAVIOR OF ORBITS CLOSE TO A HETEROCLINIC CONTOUR

1996 ◽  
Vol 06 (01) ◽  
pp. 69-79 ◽  
Author(s):  
M. BLÁZQUEZ ◽  
E. TUMA
Keyword(s):  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Chua’S Circuit ◽  
Closed Contour ◽  
Chua's Circuit ◽  
Infinite Dimensional ◽  
Focus Type

We study the behavior of the solutions in a neighborhood of a closed contour formed by two heteroclinic connections to two equilibrium points of saddle-focus type. We consider both the three-dimensional case, as in the well-known Chua's circuit, as well as the infinite-dimensional case.

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