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.

FREQUENCY DOMAIN METHOD FOR THE DICHOTOMY OF MODIFIED CHUA'S EQUATIONS

2005 ◽  
Vol 15 (08) ◽  
pp. 2485-2505 ◽  
Author(s):  
ZHISHENG DUAN ◽  
JIN-ZHI WANG ◽  
LIN HUANG
Keyword(s):  
Computer Simulation ◽  
Limit Cycles ◽  
Chaotic Attractors ◽  
Output Coupling ◽  
Frequency Domain Method ◽  
Chua’S Circuit ◽  
Single Variable ◽  
Nonlinear Functions ◽  
Chua's Circuit ◽  
Input And Output

On condition of dichotomy, it is pointed out that in Lorenz and a kind of Rössler-like system chaotic attractors or limit cycles will disappear if nonlinearity of the product of two variables is replaced by some single variable nonlinearity, for example, nonlinearity of Chua's circuit. Furthermore, an extended Chua's circuit with two nonlinear functions is presented. By computer simulation it is shown that oscillating phenomena in the extended Chua's circuit are richer than the single Chua's circuit. The corresponding extension for smooth Chua's equations is also considered. The effects of input and output coupling are analyzed for the extended Chua's circuit.

CONTROLLING CHAOS AND HYPERCHAOS BY SWITCHING MODULATION OF SYSTEMS PARAMETERS

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2686-2690 ◽  
Author(s):  
XIAO-SHU LUO ◽  
BING-HONG WANG ◽  
GUAN-RONG CHEN ◽  
PIN-QUN JIANG ◽  
JIN-QING FANG ◽  
...  
Keyword(s):  
Nonlinear System ◽  
Numerical Simulations ◽  
Control Method ◽  
Sixth Order ◽  
Chua’S Circuit ◽  
Third Order ◽  
Controlling Chaos ◽  
Chua's Circuit ◽  
The Third ◽  
New Strategy

In this paper, a new strategy is developed for controlling chaos and hyperchaos in a nonlinear system via switching modulation of systems parameters. The control method is illustrated by examples of the third-order chaotic Chua's circuit and a sixth-order coupled hyperchaotic Chua's circuit. Numerical simulations show that this method is very effective.

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.

scholarly journals Bipartite Consensus of High-Order Edge Dynamics on Coopetition Multiagent Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Yilong Yang ◽  
Zhijian Ji ◽  
Lei Tian ◽  
Huizi Ma ◽  
Qingyuan Qi
Keyword(s):  
Multiagent Systems ◽  
Line Graph ◽  
Sufficient Conditions ◽  
High Order ◽  
Third Order ◽  
Positive Weight ◽  
The Third ◽  
Initial Graph ◽  
Strongly Connected ◽  
Bipartite Consensus

The bipartite consensus of high-order edge dynamics is investigated for coopetition multiagent systems, in which the cooperative and competitive relationships among agents are characterized by positive weight and negative weight, respectively. By mapping the initial graph to a line graph, the distributed control protocol is proposed for the strongly connected, digon sign-symmetric structurally balanced line graph; and then we give sufficient conditions for the third-order multi-gent system to achieve both the bipartite consensus of edge dynamics and the final value of bipartite consensus. By transforming the coefficients of characteristic polynomial from complex domain to real number domain, the sufficient conditions for the bipartite consensus of high-order edge dynamics are also proposed, and the final values of the high-order edge dynamics on multiagent systems are obtained.

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.

CHARACTERISATION OF CHAOS IN CHUA'S OSCILLATOR IN TERMS OF UNSTABLE PERIODIC ORBITS

1993 ◽  
Vol 03 (02) ◽  
pp. 411-429 ◽  
Author(s):  
MACIEJ J. OGORZAŁEK ◽  
ZBIGNIEW GALIAS
Keyword(s):  
Periodic Orbits ◽  
Picture Book ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit ◽  
Chua’S Oscillator ◽  
Canonical Chua’S Circuit

We present a picture book of unstable periodic orbits embedded in typical chaotic attractors found in the canonical Chua's circuit. These include spiral Chua's, double-scroll Chua's and double hook attractors. The "skeleton" of unstable periodic orbits is specific for the considered attractor and provides an invariant characterisation of its geometry.

A SYSTEMATIC APPROACH TO GENERATING N-SCROLL ATTRACTORS

2002 ◽  
Vol 12 (12) ◽  
pp. 2907-2915 ◽  
Author(s):  
GUO-QUN ZHONG ◽  
KIM-FUNG MAN ◽  
GUANRONG CHEN
Keyword(s):  
Systematic Approach ◽  
Building Blocks ◽  
Chaotic Attractors ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Nonlinear Resistor ◽  
Construction Scheme ◽  
Break Points ◽  
Set Up

A new circuitry design based on Chua's circuit for generating n-scroll attractors (n = 1, 2, 3, …) is proposed. In this design, the nonlinear resistor in Chua's circuit is constructed via a systematical procedure using basic building blocks. With the proposed construction scheme, the slopes and break points of the v–i characteristic of the circuit can be tuned independently, and chaotic attractors with an even or an odd number of scrolls can be easily generated. Distinct attractors with n-scrolls (n = 5, 6, 7, 8, 9, 10) obtained with this simple experimental set-up are demonstrated.

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