A universal circuit for studying chaotic phenomena

1995 ◽  
Vol 353 (1701) ◽  
pp. 65-84 ◽  
Keyword(s):  
Dynamical Systems ◽  
Electronic Circuit ◽  
Chaotic Phenomena ◽  
Chua’S Oscillator ◽  
Potential Applications ◽  
Chaotic Electronic Circuit

In this paper, an overview of the results on an autonomous chaotic electronic circuit, called Chua’s oscillator, is given. Along with brief descriptions of numerical and analytical investigations on Chua’s oscillator, we present some of its potential applications. The significance of the oscillator for the study of general dynamical systems is discussed.

A UNIFIED FRAMEWORK FOR SYNCHRONIZATION AND CONTROL OF DYNAMICAL SYSTEMS

1994 ◽  
Vol 04 (04) ◽  
pp. 979-998 ◽  
Author(s):  
CHAI WAH WU ◽  
LEON O. CHUA
Keyword(s):  
Dynamical Systems ◽  
Chaotic Systems ◽  
Main Tool ◽  
Lyapunov Stability Theory ◽  
Asymptotical Stability ◽  
Unified Framework ◽  
Partial Synchronization ◽  
Chua’S Oscillator ◽  
And Control

In this paper, we give a framework for synchronization of dynamical systems which unifies many results in synchronization and control of dynamical systems, in particular chaotic systems. We define concepts such as asymptotical synchronization, partial synchronization and synchronization error bounds. We show how asymptotical synchronization is related to asymptotical stability. The main tool we use to prove asymptotical stability and synchronization is Lyapunov stability theory. We illustrate how many previous results on synchronization and control of chaotic systems can be derived from this framework. We will also give a characterization of robustness of synchronization and show that master-slave asymptotical synchronization in Chua’s oscillator is robust.

High-speed automated atomic absorption spectrophotometry.

1978 ◽  
Vol 24 (2) ◽  
pp. 344-347 ◽  
Author(s):  
C H McMurray ◽  
W J Blanchflower
Keyword(s):  
Atomic Absorption ◽  
High Speed ◽  
Electronic Circuit ◽  
Atomic Absorption Spectrophotometry ◽  
Atomic Absorption Spectrophotometer ◽  
Automated System ◽  
Modes Of Operation ◽  
Absorption Spectrophotometry ◽  
Potential Applications ◽  
Read Signal

Abstract We describe an integrated automated system for the atomic absorption spectrophotometer. The system makes use of a light-dependent resistor to detect the presence of a marker ion which is present along with the sample ion in the flame. An electronic circuit has been developed which enables the marker ion to trigger the read signal of the spectrophotometer. The system has been tested by determining magnesium and calcium in serum. Alternative modes of operation and different potential applications are discussed.

DYNAMICS OF THE MUTHUSWAMY–CHUA SYSTEM

2013 ◽  
Vol 23 (08) ◽  
pp. 1350136 ◽  
Author(s):  
YUANFAN ZHANG ◽  
XIANG ZHANG
Keyword(s):  
Periodic Orbit ◽  
Periodic Orbits ◽  
Chaotic Attractor ◽  
Electronic Circuit ◽  
Small Perturbations ◽  
Chaotic Phenomena ◽  
Invariant Surfaces

The Muthuswamy–Chua system [Formula: see text] describes the simplest electronic circuit which can have chaotic phenomena. In this paper, we first prove the existence of three families of consecutive periodic orbits of the system when α = 0, two of which are located on consecutive invariant surfaces and form two invariant topological cylinders. Then we prove that for α > 0 if the system has a periodic orbit or a chaotic attractor, it must intersect both of the planes z = 0 and z = -1 infinitely many times as t tends to infinity. As a byproduct, we get an example of unstable invariant topological cylinders which are not normally hyperbolic and which are also destroyed under small perturbations.

scholarly journals NONLINEAR AND COMPLEX DYNAMICS IN ECONOMICS

2014 ◽  
Vol 19 (8) ◽  
pp. 1749-1779 ◽  
Author(s):  
William A. Barnett ◽  
Apostolos Serletis ◽  
Demitre Serletis
Keyword(s):  
Dynamical Systems ◽  
Complex Dynamics ◽  
State Of The Art ◽  
Geometric Approach ◽  
Stable Region ◽  
Physical Sciences ◽  
Dynamical Complexity ◽  
Policy Relevance ◽  
Potential Applications ◽  
Transcritical Bifurcations

This paper is an up-to-date survey of the state of the art in dynamical systems theory relevant to high levels of dynamical complexity, characterizing chaos and near-chaos, as commonly found in the physical sciences. The paper also surveys applications in economics and finance. This survey does not include bifurcation analyses at lower levels of dynamical complexity, such as Hopf and transcritical bifurcations, which arise closer to the stable region of the parameter space. We discuss the geometric approach (based on the theory of differential/difference equations) to dynamical systems and make the basic notions of complexity, chaos, and other related concepts precise, having in mind their (actual or potential) applications to economically motivated questions. We also introduce specific applications in microeconomics, macroeconomics, and finance and discuss the policy relevance of chaos.

Emulating “Chaos + Chaos = Order” in Chen’s Circuit of Fractional Order by Parameter Switching

2016 ◽  
Vol 26 (06) ◽  
pp. 1650096 ◽  
Author(s):  
Wallace K. S. Tang ◽  
Marius-F. Danca
Keyword(s):  
Fractional Order ◽  
Electronic Circuit ◽  
Chaotic Circuit ◽  
Chen System ◽  
Potential Applications ◽  
Simulation And Experiment ◽  
Averaged Model ◽  
First Time ◽  
Important Design ◽  
Parameter Switching

In this paper, the effect of the parameter switching (PS) algorithm in a fractional order chaotic circuit is investigated both in simulation and experiment. The Chen system of fractional order is focused and realized in an electronic circuit. By designing a switching circuit, the PS algorithm is implemented and it is the first time, the paradoxical “Chaos [Formula: see text] Chaos [Formula: see text] Order” is presented in an electronic circuit. Both the simulation and experimental results confirm that the obtained attractor under switching approximates the attractor of the time-averaged model. Some important design issues for the circuitry realization of the PS scheme are pointed out. Finally, our work confirms the practical usage of PS algorithm in potential applications such as attractor synthesis and chaos control.

scholarly journals Chua's oscillator: A compendium of chaotic phenomena

1994 ◽  
Vol 331 (6) ◽  
pp. 705-741 ◽  
Author(s):  
Ladislav Pivka ◽  
Chai Wah Wu ◽  
Anshan Huang
Keyword(s):  
Chaotic Phenomena ◽  
Chua’S Oscillator

THEORY AND EXPERIMENT OF A FIRST-ORDER CHAOTIC DELAY DYNAMICAL SYSTEM

2013 ◽  
Vol 23 (06) ◽  
pp. 1330020 ◽  
Author(s):  
TANMOY BANERJEE ◽  
DEBABRATA BISWAS
Keyword(s):  
Time Delay ◽  
Electronic Circuit ◽  
Stable Limit Cycle ◽  
Nonlinear Behavior ◽  
Mathematical Function ◽  
Hyperchaotic System ◽  
Stable Limit ◽  
System Parameters ◽  
Chaotic Electronic Circuit ◽  
Theory And Experiment

We report the theory and experiment of a new time-delayed chaotic (hyperchaotic) system with a single scalar time delay and a nonlinearity described by a closed form mathematical function. Detailed stability and bifurcation analyses establish that with the suitable delay and system parameters, the system shows a stable limit cycle through a supercritical Hopf bifurcation. Numerical simulations exemplify that the system depicts mono-scroll and double-scroll chaos and hyperchaos for a range of delay and other system parameters. Nonlinear behavior of the system is characterized by Lyapunov exponents and Kaplan–Yorke dimension. It is established that, for some suitably chosen system parameters, the system shows hyperchaos even for a small or moderate time delay. Finally, the system is implemented in an analogue electronic circuit using off-the-shelf circuit elements. It is shown that the behavior of the time delay chaotic electronic circuit qualitatively agrees well with our analytical and numerical results.

Experimental verification of horseshoes from electronic circuits

1995 ◽  
Vol 353 (1701) ◽  
pp. 59-64 ◽  
Keyword(s):  
Dynamical Systems ◽  
Real Time ◽  
Experimental Verification ◽  
Electronic Circuit ◽  
Nonlinear Dynamical Systems ◽  
Electronic Circuits ◽  
Poincaré Maps ◽  
Nonlinear Dynamical ◽  
Poincare Maps ◽  
Return Maps

Poincaré maps are an important tool in analysing the behaviour of nonlinear dynamical systems. If the system to be investigated is an electronic circuit or can be modelled by an electronic circuit, these maps can be visualized on an oscilloscope thereby facilitating real-time investigations. In this paper, sequences of return maps eventually leading to horseshoes are described. These maps are experimentally taken both from non-autonomous and autonomous circuits.

True Random Source from Integratable Chaotic Circuits

2017 ◽  
Vol 2017 (DPC) ◽  
pp. 1-26
Author(s):  
Ned Corron ◽  
Marko Milosavljevic ◽  
Jon Blakely
Keyword(s):  
High Speed ◽  
Analog Circuit ◽  
Electronic Circuit ◽  
Random Number ◽  
Random Number Generator ◽  
Number Generator ◽  
Small Footprint ◽  
Chaotic Circuits ◽  
Chaotic Electronic Circuit ◽  
Markov Properties

In this talk, we describe a chaotic electronic circuit designed to realize a physical random number generator that is easily integrated. The small footprint of the circuit enables massive parallel realization to achieve high-speed, true-random bit sequences. The analog circuit can be fully characterized, and conjugacy to a symbolic shift proves the presence of chaos. The symbolic representation also provides a rigorous means to extract the maximum entropy from the chaotic device. Analysis of the circuit dynamics reveals critical tunings that yield special Markov properties, which are essential for removing correlations in the random sequences. Practically important is the presence of a sensitive circuit statistic that enables efficient feedback control to the Markov tuning. Numerical simulation and breadboard experimental results demonstrate the effectiveness of the proposed physical random number generator device.

MEMRISTIVE CHAOTIC CIRCUITS BASED ON CELLULAR NONLINEAR NETWORKS

2012 ◽  
Vol 22 (03) ◽  
pp. 1250070 ◽  
Author(s):  
ARTURO BUSCARINO ◽  
LUIGI FORTUNA ◽  
MATTIA FRASCA ◽  
LUCIA VALENTINA GAMBUZZA ◽  
GREGORIO SCIUTO
Keyword(s):  
High Speed ◽  
Electronic Circuit ◽  
Nonlinear Circuits ◽  
Chaotic Attractors ◽  
Associative Memories ◽  
Biological Models ◽  
Memristive Device ◽  
Nonlinear Networks ◽  
Chaotic Circuits ◽  
Chaotic Electronic Circuit

Memristors are gaining increasing interest in the scientific community for their possible applications, e.g. high-speed low-power processors or new biological models for associative memories. Due to the intrinsic nonlinear characteristic of memristive devices, it is possible to use them in the design of new dynamical circuits that are able to show complex behavior, like chaos. In this paper, two new memristive chaotic circuits are presented discussing, in particular, an approach based on Cellular Nonlinear Networks for the implementation of the memristive device. The approach investigated in this paper allows to obtain memristors with common off-the-shelf components and to observe the onset of new chaotic attractors in nonlinear circuits with memristors. Furthermore, the circuits presented in this paper, being the first examples of memristive chaotic circuits based on CNNs, can be considered as the link between the three inventions by Leon O. Chua, i.e. the memristor, the first chaotic electronic circuit and Cellular Nonlinear Networks.

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