The theory of chua s circuit chaotic dynamics can be described in many different differential equations. You should read the class textbook and study these. The chuas oscillator is a simple electrical circuit, based on a nonlinear element, presenting a wide range of behaviors, including the chaotic one. The development and numerical modeling of a chua circuit as a pedagogical tool trent ziemer the physics department at the college of wooster, wooster, oh, 44691, usa dated. This circuit will be used in the experimentsof controlling chaos. Chuas circuit has been studied extensively as a prototypical electronic system lo. Chuas circuit is the simplest electronic circuit meeting these criteria. It consists of one inductor l, two capacitors c1 and c2, one resistor r, and a nonlinear negative resistance n r, called chuas diode. The scroll generators in the paper, it is shown that the inductorless chuas circuit can be used as the core to generate the chaotic behaviour for multiscroll generation. These beautiful patterns are truly chaotic and can be modeled by relatively.
The second milestone is the recent global unfolding of chuas circuit, obtained by adding a linear resistor in series with the inductor to obtain a canonical chuas circuit now generally referred to as chuas oscillator. The book is out of print, so we are posting relevant pages from the book on this website. We will call the circuit chuas circuit with transmission line. 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. It consists of one inductor l, two capacitors c1 and c2, one resistor r, and a nonlinear negative resistance n r, called chua s diode. I did this to include the 14 ohm resistance of the real 18 mh inductor used in the version of chuas circuit we discussed on pages 5 and 8. Invented by leon chua in 1983, it and is very widely used as a standard example of chaotic oscillation. Abstractthis paper reports an implementation of chuas circuit with. Chuas circuits are some of the simplest kinds of chaotic circuits. Simulation results show that the proposed methods are valid. A linear continuous feedback control of chuas circuit.
Pdf this paper proposes a novel way to look at chuas circuit and to investigate its chaotic. The circuit that chua designed has been shown to be the simplest autonomous. It is to be emphasized that these circuits are not analog com puters. Success, we can affirm that our chua circuit works.
The circuit consists of two capacitors, an inductor, a linear resistor, and a. Chua tbe genesis of chua s circuit following a nontechnical personal reminiscence of the authors conception of chua s circuit, this paper presents the systematic sequence of technical steps which the author used to design his chaotic circuit. Secure image encryption based on a chua chaotic noise generator. The genesis of chuas circuit university of california. Chaos in the chua circuit nyu tandon school of engineering. Chua s circuit is the simplest electronic circuit that exhibits classic chaotic behavior 1. 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 also known as a chua circuit is a simple electronic circuit that exhibits classic chaos theory behavior. This demonstration plots the solution of chuas equations describing a chemical reaction scheme analogous to chuas electrical circuit. Pictured is a graph of the nonperiodic orbit in chuas circuit, each dimension representing the voltage or current in a particular component of the circuit.
Chaos in electronic circuits takashi matsumoto, fellow, ieee lnvited paper. To appear in the international journal of bifurcation and chaos in dec. I am currently working on a bifurcation diagram for chua s circuit but i am having trouble coming up with code for a bifurcation of a system of equations. The applet shows a simulation of chuas circuit, plotting the voltage measured across c1 against the voltage measured across c2. Chua s standard circuit is a simple nonlinear circuit, producing chaotic behaviour for a specific set of component. Implementation of chuas circuit with a cubic nonlinearity circuits. Jun 20, 2016 chua s circuit also known as a chua circuit is a simple electronic circuit that exhibits classic chaos theory behavior. Introduction to chuas circuit a schematic of chuas circuit is shown in figure 1. The development and numerical modeling of a chua circuit as a. The circuit that chua designed has been shown to be the simplest autonomous electronic circuit capable of exhibiting chaotic behavior. The nonlinear resistor is implemented by two linear resistors and two diodes. This corresponds to the display on an xy oscilloscope with probes connected across these capacitors. Chua circuit paradigm file exchange matlab central. And when you want to do more, subscribe to acrobat pro dc.
Introduction to chua s circuit a schematic of chua s circuit is shown in figure 1. Using an oscilloscope you can witness a chua s circuit create the strange attractor known as the double scroll. We encourage the reader to consult the references for the mathematical details of chua s circuit and chaos. Finally, some concluding remarks are given in section 4. Chuas circuit diagrams, equations, simlulations and how. The chaotic true random number generator ctrng engine of the proposed system is based on a chuas circuit. Simplest ode equivalents of chuas equations 3 universal paradigm for chaos. Chua s circuit is also the simplest physical system in which chaos can be observed 5, and it is able to create a large number of structures of many different patterns and sizes 6. A paradigm for chaos world scientific series in nonlinear science on free shipping on qualified orders.
Pdf linear and nonlinear circuits semantic scholar. The chaotic true random number generator ctrng engine of the proposed system is based on a chua s circuit. The theory of chuas circuit chaotic dynamics can be described in many different differential equations. It is solely the nonlinear resistor that makes chuas circuit nonlinear. A chaotic chemical reaction scheme derived from chuas. Mar 12, 2012 these tools allow students, hobbyists, and professional engineers to design and analyze analog and digital systems before ever building a prototype. Then you can edit, export, and send pdfs for signatures.
The anatomy of the chua circuit bachelor thesis equivalent to 15 ects jakob lavrod supervisor. This circuit is most significant because it is structurally the simplest it. Simulating the inductorless chua circuit i simulated the inductorless chua circuit shown in the schematic above with one slight modification. Apr 28, 2014 the chua circuit is the simplest electronic circuit exhibiting chaos, and many wellknown bifurcation phenomena, as verified from numerous laboratory experiments, computer simulations, and rigorous mathematical analysis. It is a very simple circuit that consists of two resistors, two capacitors, one inductance and one diode. Chaos and synchronization through the study of two coupled. Only with adobe acrobat reader you can view, sign, collect and track feedback, and share pdfs for free. Then, the receiver circuit design is detailed in section 3 where the reconstruction of the unknown information is illustrated.
Using an oscilloscope you can witness a chuas circuit create the strange attractor known as the double scroll. Chua s circuit is the simplest possible electronic circuit that can exhibit chaotic behavior. Find, read and cite all the research you need on researchgate. 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. Experimental characterization of chuas circuit patrick chang,1 edward coyle,1 john parker,1 and majid sodagar2 1school of physics, georgia institute of technology, atlanta, georgia 30332, usa 2school of electrical and computer engineering, georgia institute of technology, atlanta, georgia 30332, usa dated. Chuas book titled linear and nonlinear circuits coauthors. 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. This is the standard chua s circuit used in research and a number of experiments, but there are many different ways to realize the full circuit. Chua circuit equations california institute of technology. Secure image encryption based on a chua chaotic noise.
Implementation of chuas circuit with a cubic nonlinearity. We investigated inductorless versions of chua s circuit here is the eecs technical report, memristorbased chaotic circuits here is the eecs technical report and rigorous proof of chaos in a version of chua s circuit with only 4elements. Chuas circuit is a simple electronic network which exhibits a variety of bifurcation phenomena and attractors. We encourage the reader to consult the references for the. Pdf numerical simulation of chuas circuit oriented to circuit. This device is not a single electronic component but a nonlinear active circuit built using op amps. All the components for chuas circuit are standard, offtheshelf items except for the negative nonlinear resistor. With this powerful tool the qualitative behavior of the chua circuit can be easily visualized.
Actively working on chaotic circuits, chuas circuit to be specific. Circuit simulation of an analog secure communication based. An example of an electrical circuit,which is used in this research, is chua s circuit. Actively working on chaotic circuits, chua s circuit to be specific. Chua s circuits are some of the simplest kinds of chaotic circuits. The applet shows a simulation of chua s circuit, plotting the voltage measured across c1 against the voltage measured across c2. Heteroclinic orbits arising from coupled chuas circuits. Chua s circuit also known as a chua circuit is a simple electronic circuit that exhibits classic chaotic behavior. December 10, 2014 the electrical circuit created by and named for leon chua was constructed using discrete components and then compared with two computational models. This innocent looking circuit received a great deal of attention in the 90s in the study of complex nonlinear dynamical phenomena, and has been a leading example. So, we have managed to create chaos inside an electronic circuit, next questions is.
The development and numerical modeling of a chua circuit. Experimental characterization of nonlinear dynamics from chuas circuit john parker,1 majid sodagar,1 patrick chang,1 and edward coyle1 school of physics, georgia institute of technology, atlanta, georgia 30332, usa dated. The chua s oscillator is a simple electrical circuit, based on a nonlinear element, presenting a wide range of behaviors, including the chaotic one. A feedback control method and an adaptive feedback control method are proposed for chuas circuit chaos system, which is a simple 3d autonomous system.
Chuas circuit 10 years later chua 1994 international. The circuit diagram shows one common implementation. This demonstration plots the solution of chua s equations describing a chemical reaction scheme analogous to chua s electrical circuit. Based on your location, we recommend that you select. This circuit is most significant because it is structurally the simplest it contains only 6 circuit elements but. A stepbystep procedure to build chuas circuit using easily available and. Kennedys circuit uses tl082 opamps and utilizes a different form of chuas diode than did juhoeric.
They are considered to be a classic example of true chaos due to their design and output. I added a 14 ohm resistor between r7 and the c2r node junction. Chua s circuit is a simple electronic network which exhibits a variety of bifurcation phenomena and attractors. Chuas circuit is the simplest electronic circuit that exhibits classic chaotic behavior 1. The rich dynamic behavior of a chua circuit has been analyzed by determining the stability properties of the equilibria and a poincar. Chaotic pulse position modulation to improve the efficiency of sonar sensors. 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.
A consequence of i is that the interested reader can build, and then see and even listen to chaos. Online schematic capture lets hobbyists easily share and discuss their designs, while online circuit simulation allows for quick design iteration and accelerated learning about electronics. 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. An example of an electrical circuit,which is used in this research, is chuas circuit. The second milestone is the recent global unfolding of chuas circuit obtained by adding a linear resistor in series with the inductor to obtain a canonical chua circuitnow generally referred to as chuas oscillator. Experimental characterization of nonlinear dynamics from. Implementation of chua s circuit with a cubic nonlinearity guoqun zhong abstractthis paper reports an implementation of chua s circuit with a smooth nonlinearity, described by a cubic polynomial. Inductorless realization of chuas circuit international journal of.
The circuit consists of three energy storing elements two capacitors c1 and c2. The shape of its orbits is called a double scroll, in the center of each half is the attractor. As shown in the figure, the energy storage elements are two capacitors labeled c1 and c2 and an inductance labeled l1. Chuas circuit also known as a chua circuit is a simple electronic circuit that exhibits classic chaotic behavior. Simple electronic circuits may exhibit chaotic behavior. Chua s circuit is the simplest electronic circuit meeting these criteria. The electrical circuit depicted in figure 1 is known as the chua circuit. Chuas circuit diagrams, equations, simlulations and how to build. An inductorfree realization of the chuas circuit based on. 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. Implementation of chuas circuit with a cubic nonlinearity guoqun zhong abstractthis paper reports an implementation of chuas circuit with a smooth nonlinearity, described by a cubic polynomial. I am currently working on a bifurcation diagram for chuas circuit but i am having trouble coming up with code for a bifurcation of a system of equations. These tools allow students, hobbyists, and professional engineers to design and analyze analog and digital systems before ever building a prototype. We investigated inductorless versions of chuas circuit here is the eecs technical report, memristorbased chaotic circuits here is the eecs technical report and rigorous proof of chaos in a version of chuas circuit with only 4elements.
This circuit is most significant because it is structurally the simplest it contains only six circuit elements but. Ee100 lecture notes university of california, berkeley. There are many variations on how to build chuas circuit, but figure a shows the basic design. Sven aberg vt 2014 division of mathematical physics department of physics. Chaos and synchronization through the study of two. Chuas circuit as a musical oscillator chaoscillation. Circuit simulation of an analog secure communication based on. The chua circuit is the simplest electronic circuit exhibiting chaos, and. Chen and dong ll, 121 controlled the chaotic trajectory of the circuit to reach the limit cycle by using a linear feedback control. Chuas standard circuit is a simple nonlinear circuit, producing chaotic behaviour for a specific set of component. By applying the inputoutput and statespace techniques. Scroll generation with inductorless chuas circuit and wien. There are many variations on how to build chua s circuit, but figure a shows the basic design. This means roughly that it is a nonperiodic oscillator.
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