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.

A NOVEL APPROACH FOR CONSTRUCTING HIGH-ORDER CHUA'S CIRCUIT WITH MULTI-DIRECTIONAL MULTI-SCROLL CHAOTIC ATTRACTORS

2013 ◽  
Vol 23 (02) ◽  
pp. 1350022 ◽  
Author(s):  
CHUN HUA WANG ◽  
HAO XU ◽  
FEI YU
Keyword(s):  
High Order ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Nonlinear Functions ◽  
Third Order ◽  
Chua's Circuit ◽  
Controlled Source ◽  
The Third ◽  
Novel Approach ◽  
Rc Structure

A novel approach for constructing a high-order Chua's circuit is proposed. Based on a dual-port RCL network, a high-order Chua's circuit which can generate multi-directional multi-scroll (MDMS) chaotic attractors can be realized by introducing a RC structure and suitable nonlinear functions. First, a fourth-order Chua's circuit is achieved by adding a capacitor, a resistance and a controlled-source constituted by stair functions in the third-order Chua's circuit. And then, this recursive method can be adopted in higher-order Chua's circuit which can generate multi-scroll chaotic attractors in more directions. Finally, a sixth-order Chua's circuit is designed and its experimental results demonstrate the feasibility of this method.

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 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.

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.

KNOTTED PERIODIC ORBITS IN CHUA’S CIRCUIT

1994 ◽  
Vol 04 (03) ◽  
pp. 609-621
Author(s):  
Lj. KOCAREV ◽  
Z. TASEV ◽  
D. DIMOVSKI ◽  
L.O. CHUA
Keyword(s):  
Periodic Orbits ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Topological Properties ◽  
Chua's Circuit ◽  
Spiral Type ◽  
Lower Period

Induced templates for two members of Chua’s attractors: spiral-type and double-scroll chaotic attractors are computed using the orbits of lower period. The template describes the topological properties of periodic orbits embedded in the attractor. It is identified by a set of integers which characterize the attractor. The templates are confirmed by investigating orbits of higher period.

THE THEORY OF CONFINORS IN CHUA’S CIRCUIT: ACCURATE ANALYSIS OF BIFURCATIONS AND ATTRACTORS

1993 ◽  
Vol 03 (02) ◽  
pp. 333-361 ◽  
Author(s):  
RENÉ LOZI ◽  
SHIGEHIRO USHIKI
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Method ◽  
Phase Portrait ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Bifurcation Diagrams ◽  
Accurate Analysis ◽  
Chua's Circuit

We apply the new concept of confinors and anti-confinors, initially defined for ordinary differential equations constrained on a cusp manifold, to the equations governing the circuit dynamics of Chua’s circuit. We especially emphasize some properties of the confinors of Chua’s equation with respect to the patterns in the time waveforms. Some of these properties lead to a very accurate numerical method for the computation of the half-Poincaré maps which reveal the precise structures of Chua’s strange attractors and the exact bifurcation diagrams with the help of a special sequence of change of coordinates. We also recall how such accurate methods allow the reliable numerical observation of the coexistence of three distinct chaotic attractors for at least one choice of the parameters. Chua’s equation seemssurprisingly rich in very new behaviors not yet reported even in other dynamical systems. The application of the theory of confinors to Chua’s equation and the use of sequences of Taylor’s coordinates could give new perspectives to the study of dynamical systems by uncovering very unusual behaviors not yet reported in the literature. The main paradox here is that the theory of confinors, which could appear as a theory of rough analysis of the phase portrait of Chua’s equation, leads instead to a very accurate analysis of this phase portrait.

New Discontinuity-Induced Bifurcations in Chua's Circuit

2015 ◽  
Vol 25 (06) ◽  
pp. 1550090 ◽  
Author(s):  
Shihui Fu ◽  
Qishao Lu ◽  
Xiangying Meng
Keyword(s):  
Dynamical Systems ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Chua’S Circuit ◽  
Jacobian Matrices ◽  
Chua's Circuit ◽  
Before And After ◽  
Boundary Equilibrium ◽  
Discontinuous Bifurcations ◽  
Nonsmooth Dynamical Systems

Chua's circuit, an archetypal example of nonsmooth dynamical systems, exhibits mostly discontinuous bifurcations. More complex dynamical phenomena of Chua's circuit are presented here due to discontinuity-induced bifurcations. Some new kinds of classical bifurcations are revealed and analyzed, including the coexistence of two classical bifurcations and bifurcations of equilibrium manifolds. The local dynamical behavior of the boundary equilibrium points located on switch boundaries is found to be determined jointly by the Jacobian matrices evaluated before and after switching. Some new discontinuous bifurcations are also observed, such as the coexistence of two discontinuous and one classical bifurcation.

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