Chuas circuit is a simple electronic circuit that exhibits classic chaotic behavior. In section 4, we show how the changes in the dynamics of the circuit affects first return maps, symbolic planes and fragmentation patterns. This autonomous circuit is described by the system 1. By adding a linear resistor in series with the inductor, we obtain chuas oscillator 3, shown in fig. A new technique for chaos prediction in rf circuit design. The chua circuit can be accurately modeled by means of a set of three nonlinear ordinary differential equations in the. Chuas circuit consists of four linear elements and one nonlinear resistor nrthe socalled chuas diode, whose possible fivesegmented iv characteristic is given by the formula 2 and shown in fig. Chaos synchronization and transmission of information. 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. For a good hour he sits on the stage of the lecture room of the museum for modern art in. Implementation of chuas circuit with a cubic nonlinearity circuits.
Chuas circuit diagrams, equations, simlulations and how. For the modified chuas circuit, there have been several controllers proposed to suppress the chaos. Chen and dong, applied the linear feedback control for guiding the chaotic trajectory of the circuit to limit cycle. We discuss the hyperbolic regime and show that the evolution of this circuit is very similar to onedimensional systems with homoclinic chaos. This circuit, known for its rich repertoire of nonlinear dynamical phenomena and has become a universal paradigm for chaos. Chaos, along with quantum mechanics and relativity, has been hailed as one of the major discoveries of 20th century. Implementation of the chua s circuit and its applications. Chuas circuit also known as a chua circuit is a simple electronic circuit that exhibits classic chaotic behavior. Stability analysis, periodadding, basin of attraction metamorphoses. An inductorfree realization of the chuas circuit based. Implementation of chuas circuit with a cubic nonlinearity. Hartley suggested that the piecewise linear function can be replaced by a cubic polynomial with no major change in the systems dynamic characteristics. Chua tbe genesis of chuas circuit following a nontechnical personal reminiscence of the authors conception of chuas circuit, this paper presents the systematic sequence of technical steps which the author used to design his chaotic 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. A paradigm for chaos world scientific series on nonlinear science series b book online at best prices in india on. Chaos synchronization and transmission of information in. Gilli and maggio 2 proposed an attractive analytical approach, based on the work of. To appear in the international journal of bifurcation and chaos in dec. They are considered to be a classic example of true chaos due to their design and output. The lorenz attractor, a paradigm for chaos 3 precision. There are many variations on how to build chuas circuit, but figure a shows the basic design. An example of an electrical circuit,which is used in this research, is chuas circuit. Search for library items search for lists search for contacts search for a library. Chuas circuit has been studied extensively as a prototypical electronic system. Implementation of chuas chaotic circuit using current feedback opamps article pdf available in electronics letters 349.
This corresponds to the display on an xy oscilloscope with probes connected across these capacitors. Fundamental theory and applications, ieee transactions on circuits and systems i. A circuit implementation of the designed feedback control is realized by adding a linear resistor and an appropriate. A paradigm for chaos, world scientific, singapore, 1993 on chuas circuit have been published since its inception a decade ago. Yet, the theory would be rather poor if it was limited to this absence of determinism and did not encompass any deductive aspect. Simulating chuas circuit return to table of contents first we need to simulate chuas circuit. The negative side of chuas circuit parameter space. Chuas circuit is a paradigm in nonlinear dynamics and. Periodicity and chaos in chuas circuit guoqun zhong and f. Ayrom eecs department university of california, berkeley technical report no. Chuas circuit is one of the most important electronic devices that are used for chaos and bifurcation studies. Chuas circuit is a simple electronic circuit that exhibits classic chaos theory behavior.
Designing chaotic mathematical circuits for solving. Here is the multisim schematic, click for a screen shot. 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. A central role of secure communication is devoted to it. The timedelayed chuas circuit tdcc, exhibiting a homoclinic route to chaos, is a particular example of a circuit whose dynamic at high frequencies is hard to investigate by means of timedomain simulations. Chua, who was a visitor at waseda university in japan at that time. 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. Chuas circuits are some of the simplest kinds of chaotic circuits. Chuas circuit is a paradigm for chaos which is considered as the simplest nonlinear electrical circuit that exhibits almost known chaotic phe. The synthesis and practical realization of chaotic deterministic dynamical systems in the form of lumped electronic circuits is an old and well. Piecewiselinear chaotic systems with a single equilibrium point tao yang and leon o. 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. More than 200 papers, two special issues journal of circuits, systems, and computers, march, june, 1993, and ieee trans. Background the chuas circuit a thirdorder autonomous, dissipative electrical circuit has been investigated thoroughly at the experimental, numerical and analytical levels.
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. On the contrary, i want to insist on the fact that, by asking the good questions, the theory is able to. 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. Chuas circuit 10 years later chua 1994 international journal of. Chua, who was a visitor of waseda university japan at that time matsumoto 1984. The analogous circuit is implemented and used to perform an experimental mapping of a large variety of attractors, where the perfect match between experiment and. 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. A paradigm for chaos world scientific series in nonlinear science on free shipping on qualified orders.
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. Adaptive control and synchronization of a modified chuas. 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. The ease of construction of the circuit has made it a ubiquitous realworld example of a chaotic system, leading. Experimental confirmation of chaos from chuas circuit. Chaos in the orbits of giant planets jupiter, saturn and uranus the location of these planets cannot be predicted on a time scale longer than. This means roughly that it is a nonperiodic oscillator. Following the worldwide tradition of use of chuas circuits for various purposes, we introduce the paradigm of chaotic mathematical circuitry. The applet shows a simulation of chuas circuit, plotting the voltage measured across c1 against the voltage measured across c2. This circuit will be used in the experimentsof controlling chaos. Finally, in section 5, we summarize our conclusions.
Chaos control of the modified chuas circuit system. International journal of bifurcation and chaos, vol. These beautiful patterns are truly chaotic and can be modeled by relatively. A circuit implementation for a cubicpolynomial chuas diode. Applying kcl and kvl, the chuas circuit is described by three differential equations. 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. Using an oscilloscope you can witness a chuas circuit create the strange attractor known as the double scroll. A universal circuit for studying and generating chaos. The theory of chuas circuit chaotic dynamics can be described in many different differential equations. 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. Revised november, 1999 as a unique paradigm for chaos, the various versions of chuas circuits and equations consists of. 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.
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. 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. However, chuas circuit provides only 3dimensional chaos, as figs. An inductorfree realization of the chuas circuit based on electronic analogy. Online identification and control of chaos in a real chuas circuit 429 system dynamics near chosen periodic orbit. These equations that describe dynamic systems have a time evolution strongly dependent on initial conditions.
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. 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 original chuas circuit contains a piecewise linear resistor. On the complete stability of nonsymmetric cellular neural networks circuits and systems i. 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. Simple sufficient conditions for the controllability of this particular circuit are established. 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.
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