The following section presents a technical version of the design episode alluded to in the proceeding narrative. Chuas circuit also known as a chua circuit is a simple electronic circuit that exhibits classic chaotic behavior. Michael peter kennedy s classic opamp implementation of chua. Chua, who was a visitor of waseda university japan at that time matsumoto 1984. Chaos and synchronization through the study of two coupled. This means roughly that it is a nonperiodic oscillator. Learning of chuas circuit attractors by locally recurrent. Online identification and control of chaos in a real chuas circuit 429 system dynamics near chosen periodic orbit. Chuas circuits are some of the simplest kinds of chaotic circuits.
By computer simulation it is shown that oscillating phenomena in the extended chuas circuit are richer than the single chuas circuit. Chuas circuit diagrams, equations, simlulations and how. Volkovskii twoparameter study of transition to chaos in chua s circuit. Furthermore,anextendedchuas circuitwith two nonlinearfunctions is presented. Practical implementation of chua s circuit with a cubic nonlinearity since the desired l i characteristic of the nonlinear resistor lv in chuas circuit is an oddsymmetric function with respect to origin, here we use the cubic polynomial 7 with the coefficients. Chuas circuit and the qualitative theory of dynamical.
Juhoeric used a different circuit to create chuas diode and used different values for some of the other circuit components compared with the reference papers listed on the previous page. The unified canonical feedback control strategy developed recently by the present authors for controlling chaotic systems is refined and applied to the wellknown chuas circuit, driving its orbits from the chaotic attractor to its unstable limit cycle. The goal is to build chuas circuit quickly and easily. Simple sufficient conditions for the controllability of this particular circuit are established. Apr 05, 2014 this video shows the sequence of bifurcations specifically, a perioddoubling cascade leading up to the chaotic single and doublescroll attractors. Chua, who was a visitor at waseda university in japan at that time.
Chaos synchronization and transmission of information in. Ieee circuits and systems society vitold belevitch award 2007, for seminal contributions to nonlinear circuit theory, the first mathematically proven physical implementation of chaos chua circuit, the local activity principle as the root of complexity, the cellular neuralnonlinear network principle and basic theory, and the qualitative. Park robust control and nonlinear dynamics laboratory, department of electrical engineering, yeungnam university, 2141 daedong, kyongsan 712749, republic of korea accepted 23 november 2004 abstract in this letter, the problem of chaos synchronization of a chaotic system. Chuas circuit definition chuas circuit is a simple electronic circuit that exhibits classic chaos theory behavior. Chua s circuit and the contemporary qualitative theory one of the reasons for the popularity of chua s circuit is that it can generate a large variety of complex dynamics, and convoluted bifurcations, from a simple model in the form of a threedimensional autonomous piecewise linear ordinary differential equation flow.
Chua s circuit also known as a chua circuit is a simple electronic circuit that exhibits classic chaotic behavior. A central role of secure communication is devoted to it. Chuas circuit chuas circuit is an autonomous system composed ofanetwork oflinearpassive elements, connected to anonlinearactive component. For uninitiated researchers, engineers, and scientists interested in a quick entry into the subject of chaos, this book offers a timely collection of 55 carefully selected papers covering almost. Adaptive control and synchronization of a modified chuas. Pdf chuas circuit and the qualitative theory of dynamical systems. Linear generalized synchronization of continuoustime chaotic systems junguo lu, yugeng xi.
Revised february 5, 1997 bifurcations and the structure of limit sets are studied for a threedimensional chuas circuit system with a cubic nonlinearity. Because chuas circuit is endowed with virtually every bifurcation phenomena reported in the extensive literature on chaos, and because it is the only chaotic. Analyzing the circuit using kirchhoffs circuit laws, the dynamics of chuas circuit can be accurately modeled by means of a system of three nonlinear ordinary differential equations in the. Chua s circuits are some of the simplest kinds of chaotic circuits. The existence of periodic traveling wave solutions has been proved recently chow et al. Chuas circuit is one of the most important electronic devices that are used for chaos and bifurcation studies. My simulation of chuas circuit using tl082 opamps i have made my own ltspice simulation of chuas circuit using the paper cited earlier by michael kennedy as a guide. Chuas circuit is an autonomous system because there is no external signal injected into the system. The chua circuit can be accurately modeled by means of a set of three nonlinear ordinary differential equations in the. To appear in the international journal of bifurcation and chaos in dec. Chaos in the chua circuit nyu tandon school of engineering. The applet shows a simulation of chuas circuit, plotting the voltage measured across c1 against the voltage measured across c2. The ease of construction of the circuit has made it a ubiquitous realworld example of a chaotic system, leading some to declare it a paradigm for chaos. Chuas circuit consists of a linear inductor l, two linear capacitors.
Pdf chuas circuit is a nonlinear dynamic circuit that has assumed a. In section 4, we show how the changes in the dynamics of the circuit affects first return maps, symbolic planes and fragmentation patterns. More than 200 papers, two special issues journal of circuits, systems, and computers, vol. Implementation of chuas circuit with a cubic nonlinearity. Finally, we take chuas circuit as an example for illustration and veri.
Chuas circuit was the first circuit implementation specially designed to exhibit chaos chua, 1984 and the first that was proved to be chaotic rigorously chua, et. The present proposal offers the advantages of low component count, current mode processing, availability of current across inductor and availability of voltage across inductor in form of current. The case of construction of the circuit has made it a ubiquitous realworld example of a chaotic system, leading some to declare it a paradigm for chaos. A universal circuit for studying and generating chaos. Read experimental confirmation of chaos from chuas circuit, international journal of circuit theory and applications on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Chaotic traveling wave solutions in coupled chuas circuits. For uninitiated researchers, engineers, and scientists interested in a quick entry into the subject of chaos, this book offers a timely collection of 55 carefully selected papers covering almost every aspect of this subject. This circuit is considered a paradigm because it is a fact that chuas circuit is the rst chaotic system in which chaos was systematically derived,chua1992 physically con rmedmatsumoto1984. Basics chuas circuit chuas circuit is a simple electronic circuit that exhibits classic chaos theory behavior. For studying a more complex chaotic behavior called hyperchaos, whichhas beenreported in hydrodynamicsand semiconductor devices, one has to combine the behavior of several chua s circuits and couple them in various ways. An inductorfree realization of the chuas circuit based on electronic analogy 391 of wienbridge 15 and inductance emulator circuits based on transistors 16, voas 17, cfoas 12, otas 18, 19 and ftfn 20.
Fundamental theory and applications, ieee transactions on author. Chuas circuit has been studied extensively as a prototypical electronic system. A synthetic inductor implementation of chuas circuit. In this paper, locally recurrent neural networks lrnns are used to learn the attractors of chua s circuit, a paradigm for studying chaos. Many practical applications of neural networks require the identification of strongly nonlinear e. Here is the multisim schematic, click for a screen shot. More than 200 papers, two special issues journal of circuits, systems, and computers, march, june, 1993, and ieee trans. Chaos synchronization of a chaotic system via nonlinear. An improved chuas circuit and its use in hyperchaotic. Online identification and control of chaos in a real chua s circuit 429 system dynamics near chosen periodic orbit. The theory of chuas circuit chaotic dynamics can be described in many different differential equations. Because chua s circuit is endowed with virtually every bifurcation phenomena reported in the extensive literature on chaos, and because it is the only chaotic system which can be easily built by a novice, simulated in a personal computer, and tractable mathematically, it has become a paradigm for chaos, and a vehicle for illustrating this. First, this version of the circuit uses the lmc6482 which is more robust and easier to obtain than the jfet opamps used. These beautiful patterns are truly chaotic and can be modeled by relatively.
Using an oscilloscope you can witness a chua s circuit create the strange attractor known as the double scroll. The circuit consists of three energy storing elements two capacitors c1 and c2. As an expansion and extension for threeorder and fourorder chuas circuit, a new method to construct a class of highorder chuas circuit and its fpga hardware implementation has been studied in this paper. A paradigm for chaos world scientific series on nonlinear science series b book online at best prices in india on. Chuas circuit chuas circuit is a simple electronic circuit that exhibits classic chaos theory behavior. An example of an electrical circuit,which is used in this research, is chuas circuit. Chaos synchronization of a chaotic system via nonlinear control ju h. This circuit, known for its rich repertoire of nonlinear dynamical phenomena and has become a universal paradigm for chaos. Once you understand the basics of nonlinear circuit analysis, here are some links and papers to get you started with chaos and chua s circuit. It explains why chua s circuit is of interest not only to radio physicists but to nonlinear scientists. Since chuas circuit is endowed with an unusually rich repertoire of nonlinear dynamical phenomena, it has become a universal paradigm for chaos. Read chua s circuit 10 years later, international journal of circuit theory and applications on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.
Experimental confirmation of chaos from chuas circuit. Applying kcl and kvl, the chuas circuit is described by three differential equations. Introduction to chuas circuit a schematic of chuas circuit is shown in figure 1. Chuas circuit is a paradigm for chaos which is considered as the simplest nonlinear electrical circuit that exhibits almost known chaotic phe. When it is determined how the circuit works, there will be explained to what extend the circuit is controlled and how it can be synchronized. These equations that describe dynamic systems have a time evolution strongly dependent on initial conditions. This circuit will be used in the experimentsof controlling chaos. The purpose of this paper is to prove the existence of chaotic traveling wave solutions for such system.
An inductorfree realization of the chuas circuit based. Chuas circuit is extensively studied from the viewpoint, of chaos, bifurcations, and multistable behaviour, and there are numerous papers on this, one of the most widely studied circuits today see, for example, 189. Experimental analysis of 1d maps from chua s circuit 580 n. However, chuas circuit provides only 3dimensional chaos, as figs. Designing chaotic mathematical circuits for solving. The nonlinear circuit theory behind chua s circuit 2.
Abstractthis paper reports an implementation of chuas circuit with a smooth. This should be enough background for you to understand the implementation of chua s circuit. In section 2 we define chaos, in the context of the deterministic chaos theory, as a consequence of peculiar properties of deterministic nonlinear ordinary differential equations nlode. Implementation of chuas circuit with a cubic nonlinearity circuits. Great howto on building chuas circuit, a simple but.
Chaos synchronization and transmission of information. A feedback control method and an adaptive feedback control method are proposed for chua s circuit chaos system, which is a simple 3d autonomous system. Chuas circuit regulation using a nonlinear adaptive. An improved implementation of chua s circuit using dual output current conveyor is presented. Among the members of chuas circuit family, the autonomous canonical chuas circuit introduced by chua and lin 1990 is of considerable importance. The initial values of the parameters used in the applet correspond to the component values in the circuit diagram, and show a simple periodic orbit oscillation.
There are many variations on how to build chuas circuit, but figure a shows the basic design. This paper provides a mathematician s perspective on chua s circuit as a paradigm for chaos. Chuas circuit is the simplest possible electronic circuit that can exhibit chaotic behavior. Renormalization group, universality and scaling 591 a.
Kennedys circuit uses tl082 opamps and utilizes a different form of chuas diode. The negative side of chuas circuit parameter space good agreement with theoretical analyses. Chuas circuit diagrams, equations, simlulations and how to build. Chuas circuit also known as a chua circuit is a simple electronic circuit that exhibits classic chaos theory behavior. Chen and dong, applied the linear feedback control for guiding the chaotic trajectory of the circuit to limit cycle. The various literature references show that the study of chaos is a universal problem.
Implementation of the chua s circuit and its applications. Nonetheless, what eric used is still truly chuas circuit. The event which led to the discovery of chuas circuit took place in the. Ayrom arracr this paper reports a perioddoubling route to chaos as ob served from a laboratory model of the simplest possible chaotic autono mous circuit. The ease of construction of the circuit has made it a ubiquitous realworld example of a chaotic system, leading some to declare it a paradigm for chaos madan 1993. Thisisbecause it is capable of realizing the behavior of every member of the chuas circuit. Chaos, along with quantum mechanics and relativity, has been hailed as one of the major discoveries of 20th century. This means roughly that is a nonperiodic oscillator. Hartley and mossayebi showed the control of modified chuas circuit systems and demonstrated how to design a controller for tracking the capacitor voltage of the system by applying the input. In this chapter, we study what is probably one of the most important contributions to chaos theory, leon o. Jun 20, 2016 chua s circuit also known as a chua circuit is a simple electronic circuit that exhibits classic chaos theory behavior. Pdf chuas circuit and the qualitative theory of dynamical. Based on the structure of a typical thirdorder chuas circuit, a fifthorder, sixthorder and seventhorder chuas circuit have been constructed through the series in thetype sub.
Finally, the conclusions of this work are presented in sec. Because of this, it has been object of much study, and appears widely referenced in the literature. Chaotic phenomena and applications at nolta 93, and a book r. We discuss the hyperbolic regime and show that the evolution of this circuit is very similar to onedimensional systems with homoclinic chaos. An inductorfree realization of the chuas circuit based on. Ayrom eecs department university of california, berkeley technical report no. The easy experimental implementation of the circuit, combined with the existence of a simple and accurate theoretical model, makes chua s circuit a useful system to study many fundamental and applied issues of chaos theory. Simulation results show that the proposed methods are valid. The applet shows a simulation of chua s circuit, plotting the voltage measured across c1 against the voltage measured across c2. A synthetic inductor implementation of chuas circuit bharathwaj muthuswamy, kyle sundqvist and tamara blain abstractwe show how to build an inductorless version of the classic chuas circuit. Since the adaptive control is used vastly in the linear systems control, here we introduce a new trend of application of adaptive method in the chaos controlling field. Chuas circuit 10 years later chua 1994 international. Chuas circuit 10 years later, international journal of. Pdf a new look at chuas circuit moez feki academia.
Finally, in section 5, we summarize our conclusions. Chaos in the chua circuit project for the course on dynamical systems department of electrical engineering eindhoven university of technology siep weiland abstract. Search for library items search for lists search for contacts search for a library. Because chuas circuit is endowed with virtually every bifurcation phenomena reported in the extensive literature on chaos, and because it is the only chaotic system which can be easily built by a novice, simulated in a personal computer, and tractable mathematically, it has become a paradigm for chaos, and a vehicle for illustrating this. The chua circuit is among the simplest nonlinear circuits that shows most complex dynamical behavior, including chaos. A useful list of links related to chua s circuit and chaos. This is the standard chuas circuit used in research and a number of experiments, but there are many different ways to realize the full circuit. Periodicity and chaos in chuas circuit guoqun zhong and f. Chuas circuit and the qualitative theory of dynamical systems. They are considered to be a classic example of true chaos due to their design and output. The asymptotical stability is proven with lyapunov theory for both of the proposed methods, and the system can be dragged to one of its three unstable equilibrium points respectively. A paradigm for chaos world scientific series in nonlinear science on free shipping on qualified orders. Linear generalized synchronization of continuoustime. Chuas circuit is a simple electronic circuit that exhibits classic chaos theory behavior.
The ease of construction of the circuit has made it a ubiquitous realworld example of a chaotic system, leading. Simulating chuas circuit return to table of contents first we need to simulate chuas circuit. In this work, we show how to build chuas circuit using offshelf components, describe the design methodology for constructing the nonlinear resistor and present the experimental and simulation results of the chuas circuit. This corresponds to the display on an xy oscilloscope with probes connected across these capacitors. Background the chuas circuit a thirdorder autonomous, dissipative electrical circuit has been investigated thoroughly at the experimental, numerical and analytical levels. The unified canonical feedback control strategy developed recently by the present authors for controlling chaotic systems is refined and applied to the wellknown chua s circuit, driving its orbits from the chaotic attractor to its unstable limit cycle. The genesis of chuas circuit university of california. Chuas equation was proved to be chaotic in two years. Chuas circuit is the simplest electronic circuit that produces chaos the output of this circuit never repeats the same sequence, and is a truly random signal. Chua chua s circuit with a discontinuous nonlinearity 622. Using an oscilloscope you can witness a chuas circuit create the strange attractor known as the double scroll. The negative side of chuas circuit parameter space.