scholarly journals CANARDS FROM CHUA'S CIRCUIT

2013 ◽  
Vol 23 (04) ◽  
pp. 1330010 ◽  
Author(s):  
JEAN-MARC GINOUX ◽  
JAUME LLIBRE ◽  
LEON O. CHUA
Keyword(s):  
Dynamical Systems ◽  
Singularly Perturbed ◽  
Fast Variable ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Flow Curvature ◽  
Cubic Model ◽  
Generic Existence

The aim of this work is to extend Benoît's theorem for the generic existence of "canards" solutions in singularly perturbed dynamical systems of dimension three with one fast variable to those of dimension four. Then, it is established that this result can be found according to the Flow Curvature Method. Applications to Chua's cubic model of dimension three and four enable to state the existence of "canards" solutions in such systems.

STRANGE ATTRACTORS IN PERIODICALLY KICKED CHUA'S CIRCUIT

2005 ◽  
Vol 15 (01) ◽  
pp. 83-98 ◽  
Author(s):  
QIUDONG WANG ◽  
ALI OKSASOGLU
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Autonomous System ◽  
Strange Attractors ◽  
External Forcing ◽  
Chua’S Circuit ◽  
New Developments ◽  
Chua's Circuit

In this paper, we discuss a new mechanism for chaos in light of some new developments in the theory of dynamical systems. It was shown in [Wang & Young, 2002b] that strange attractors occur when an autonomous system undergoing a generic Hopf bifurcation is subjected to a weak external forcing that is periodically turned on and off. For illustration purposes, we apply these results to the Chua's system. Derivation of conditions for chaos along with the results of numerical simulations are presented.

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.

Chua's Circuit and the Qualitative Theory of Dynamical Systems

1997 ◽  
Vol 07 (09) ◽  
pp. 1911-1916 ◽  
Author(s):  
Christian Mira
Keyword(s):  
Dynamical Systems ◽  
Complex Dynamics ◽  
Qualitative Theory ◽  
60Th Birthday ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Electronic Oscillators

Simple electronic oscillators were at the origin of many studies related to the qualitative theory of dynamical systems. Chua's circuit is now playing an equivalent role for the generation and understanding of complex dynamics. In honour of my friend Leon Chua on his 60th birthday.

THE EFFECTS OF SYMMETRY BREAKING IN CHUA'S CIRCUIT AND RELATED PIECEWISE-LINEAR DYNAMICAL SYSTEMS

1993 ◽  
Vol 03 (04) ◽  
pp. 963-979 ◽  
Author(s):  
CLAUS KAHLERT
Keyword(s):  
Dynamical Systems ◽  
Symmetry Breaking ◽  
Piecewise Linear ◽  
Broken Symmetry ◽  
Chua’S Circuit ◽  
Intermediate Region ◽  
Linear Dynamical Systems ◽  
Chua's Circuit ◽  
Critical Curves ◽  
Return Maps

The behavior of transfer and return maps in the intermediate region of Chua's circuit and related systems undergoes a number of changes as the symmetry of the dynamics is broken, i.e., the separating planes are moved away from symmetric positions. We employ the technique of maps induced by the flow of the system and construct the critical curves for the maps in the intermediate region of state space. The influence of a broken symmetry on the critical curves and the flow is discussed in depth. We demonstrate that any breaking of symmetry potentially weakens and eventually destroys the chaos producing mechanisms.

TWO IMPULSIVE SYNCHRONIZATION STUDIES USING SC-CNN-BASED CIRCUIT AND CHUA'S CIRCUIT

2004 ◽  
Vol 14 (09) ◽  
pp. 3277-3293 ◽  
Author(s):  
RECAI KILIÇ ◽  
MUSTAFA ALÇI ◽  
ENIS GÜNAY
Keyword(s):  
Dynamical Systems ◽  
Lorenz System ◽  
Chua’S Circuit ◽  
Cell Dynamics ◽  
Chua's Circuit ◽  
Pspice Simulation ◽  
Impulsive Synchronization ◽  
Hardware Implementations ◽  
Chaotic Circuits ◽  
Simulation Results

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.

scholarly journals Slow Invariant Manifolds of Slow–Fast Dynamical Systems

2021 ◽  
Vol 31 (07) ◽  
pp. 2150112
Author(s):  
Jean-Marc Ginoux
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Singular Perturbation ◽  
Invariant Manifolds ◽  
The Other ◽  
Singularly Perturbed ◽  
Van Der Pol ◽  
Flow Curvature ◽  
The One

Slow–fast dynamical systems, i.e. singularly or nonsingularly perturbed dynamical systems possess slow invariant manifolds on which trajectories evolve slowly. Since the last century various methods have been developed for approximating their equations. This paper aims, on the one hand, to propose a classification of the most important of them into two great categories: singular perturbation-based methods and curvature-based methods, and on the other hand, to prove the equivalence between any methods belonging to the same category and between the two categories. Then, a deep analysis and comparison between each of these methods enable to state the efficiency of the Flow Curvature Method which is exemplified with paradigmatic Van der Pol singularly perturbed dynamical system and Lorenz slow–fast dynamical system.

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