Based on two introduced lemmas, some sufficient algebraic criteria for global anti synchronization are proved and optimized in. Numeral simulation and circuit simulation show that the synchronization problem. Chaos synchronization for master slave piecewise linear. Here, experimental results are shown on the control and synchronization of chua. However, results of these software depend on numerical. Synchronization of chuas circuits with multiscroll. 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. Chaotic circuits and their digital models, respectively, can be included in any sort of cryptosystems 12. Synchronization of chaotic nonlinear circuits via a memristor. Building chuas circuit on a breadboard can be a frustrating endeavor if care is not taken. This really gives you a good look at the double scroll attractor from all angles and makes the 3dimensional nature of the output more visceral. In this paper, the hybrid synchronization is investigated for nscroll chaotic chua circuit wallace et al. I have also included a switch to conveniently turn synchronization on or off.
They are considered to be a classic example of true chaos due to their design and output. The proposed circuit has a variety of suitable real applications related to chaos encryption and cryptography. Dynamics and synchronization of memristorbased fractional. At the same time, chua s circuit became an impulse for searching for new systems of differential equations generating chaos, see for example,,,,, and for the creation of illustrative monographs. Nonlinear dynamics of chaotic attractor of chua circuit. It has also been used extensively in many numerical simulations, and exploited in avantgarde. The motivation for synchronization of a chaotic circuit is from the fact that this circuit could be used for encryption. In ths report an answer will be given to the question whether it is possible to synchronisetwo chua s circuits. Virtualization of chuas circuit state space sciencedirect. Hidden attractor in the rabinovich system, chua circuits. Chuas circuit is the simplest oscillator exhibiting a variety of bifurcations and chaos, it was introduced in 1983 by leon o. Chaos synchronization in chuas circuit chuas circuit. The dynamics analysis of the new system can also demonstrate the hyperchaotic characteristics. Eckert eecs department university of california, berkeley technical report no.
Simulation, analysis, and a linear observer of chuas circuit. However, when building this circuit at home be aware that, as a chaotic circuit, very slight variations can cause large effects or failure of the entire circuit. In this paper, chua attractors chaotic oscillator, synchronization and masking communication circuits were. Synchronization of chaos between the driver and the driven system is demonstrated. Numerical simulation chaotic synchronization of chua.
Dimensionless chuas circuit the animation on the left is taken directly from a visualization of a chuas circuit simulation in matlab after running for about 100 seconds and then rotated for viewing. The chua circuit is among the simplest nonlinear circuits that shows most complex dynamical behavior, including chaos which exhibits a variety of bifurcation phenomena and attractors. Experimentally one of the easiest systems to control and synchronize is the electronic circuit. Miller version 21 november 2019 consider chua s circuit as shown in fig. Since the birth of the chua circuit in 1983, a considerable number of fruitful, fascinating and relevant research topics have arisen. Numerical simulation chaotic synchronization 5 by reducing the variable resistor r in fig. Fengoutput tracking and synchronization of chaotic chua s circuit with disturbances via. Chua s circuit for high school students gandhi, gauruv. Circuit realization, chaos synchronization and estimation. To the best of our knowledge, this is the first attempt to implement a circuit that estimates the values of the unknown parameters of chaotic system and achieves synchronization. Synchronizing chaotic attractors of chua s canonical circuit 1963 a b fig. The master chua is unaffected by the slave circuits or the coupling and acts autonomously. Chaos and synchronization through the study of two. The design and analysis of adaptive synchronization for the new memristorbased chaotic system and its slave system are carried out.
In this paper, the synchronization problem of coupled chua s circuits generator of nscroll chaotic attractors in masterslave configuration is numerically studied. In the same paper, they also conjectured, based on simulations, that synchronization of two chua s circuits with the second state as the feedback variable can be achieved when the cou. The slave chua circuits use the coupling circuitry to synchronize to the masters signal. Simulation results are used to visualize and illustrate the effectiveness of chua chaotic system in synchronization and application of secure communication. Chaotic synchronization in small assemblies of driven chua. When two chaotic systems are not identical, synchronization becomes less trivial and various adaptive schemes are considered. After 16 iterations, the lmi constraints were found infeasible. This paper examines synchronization in chua s circuit, proven to be the simplest electronic circuit to. A loose connection or uneven voltages will dramatically affect the output. Chua, 1994 that synchronization of two chua s circuits with the rst state as the feedback variable can be achieved when the coupling constant is large enough. Chua s circuit was the first circuit implementation specially designed to exhibit chaos chua, 1984 and the first that was proved to. This circuit is composed of two capacitors, c1 and c2, two resistors r and r, one inductor l, and the nonlinear piecewise linear.
This paper examines synchronization in chua s circuit, proven to be the simplest electronic circuit to exhibit chaotic behavior. Chuas circuit is literally the simplest chaotic circuit. Several recent papers have investigated the feasibility of synchronization of chaotic systems. Chaos synchronization in chuas circuit eecs at uc berkeley. This paper presents a new output feedback technique for synchronizing chaotic circuits. This implies a good control of a chaotic system and a good synchronization between the involved systems.
Chua, who was a visitor at waseda university in japan at that time. Chua s circuits are some of the simplest kinds of chaotic circuits. Chua 7 this circuit contains a linear resistor r, r0, a single nonlinear resistor f v1, and three linear energystorage components. A new synchronization principle and application to chua s circuits yongai zheng, zengrong liu and jin zhou. In summary, the slaves synchronize to the master chua, but the master chua is unaffected. Applications the chua circuit has been built and used in many laboratories as a physical source of pseudo random signals, and in numerous experiments on synchronization studies, such as secure communication systems and simulations of brain dynamics. This paper examines synchronization in chuas circuit, proven to be the simplest electronic circuit to. Simulation, analysis, and a linear observer of chua s circuit ece 6740 nonlinear control systems d. In particular, we consider a modified chua s circuit generator of 5scroll chaotic attractors by. Our theorems on hybrid synchronization for nscroll chaotic chua circuits are established using lyapunov stability theory. Experimental realtime phase synchronized states can be. In honor of the 25th anniversary of the invention of chua s circuit, this book presents the 25 years of research on the implementation of chua s circuit, and also. For example, a fractional order chua s circuit with a memristor and a negative conduc tance have been studied in 11, and the synchronization based on memristor but limited to integerorder system has been investigated in 12 due to its potential applica.
This means roughly that it is a nonperiodic oscillator. A new memristorbased 5d chaotic system and circuit. The first mention of the chua s circuit was the global impetus not only for chaos research, but also for the use of chaos in practice. Chaos, chua s oscillator circuit, memristor, unidirectional coupling, complete synchronization. Each circuit has an additional perturbation source, the on lefthand side, the circuiti has an extra source noise, whereas on the other side the circuitii has an extra sinusoidal source. A new synchronization principle and application to chua s circuits 817 the hurwitz theorem is practicable for small n.
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. The approach is successfully applied to the recently proposed chua s circuit with xx nonlinearity. Synchronization, chaotic systems, chaotic chua s system, sliding mode observers, chaos based secure communications. But because of its simplicityand universality, this circuit is bit more special. Phase synchronization in the perturbed chua circuit. This paper proposes a new 5d chaotic system with the fluxcontrolled memristor. Chuas circuit diagrams, equations, simlulations and how. 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.
Using an oscilloscope you can witness a chua s circuit create the strange attractor known as the double scroll. Chuas circuit also known as a chua circuit is a simple electronic circuit that exhibits classic chaotic behavior. Abstract chaosbased data encryption is one of the most reliable methods used in secure communications. The perturbed chua circuit and the characteristic curve of the piecewise linear resistor rnl are schematically shown in fig. Chua, chua s circuit is a simple electronic circuit that consists of one linear resistor, two capacitors, one inductor, and one nonlinear resistor. Furthermore, the modularized circuit designs method is used in the new chaotic system. Chaos synchronization and transmission of information in.
Hidden attractor in the rabinovich system, chua circuits and pll. Chua s circuit also known as a chua circuit is a simple electronic circuit that exhibits classic chaotic behavior. System consisting of two chuas circuits coupled together. Chua s circuit has been extensively used to study various topics relating to chaos theory, including synchronization of coupled chaotic systems. Chaos synchronization for master slave piecewise linear systems. A number of recent papers have investigated the feasibility of synchronizing chaotic systems. Circuit simulation of an analog secure communication based. 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. We show experimental and numerical results of phase synchronization between the chaotic chua circuit and a small sinusoidal perturbation. Chuas circuit implementations world scientific series. Practical guide for studying chua s circuits, a by recai kilic, 97898142912, available at book depository with free delivery worldwide. These beautiful patterns are truly chaotic and can be modeled by relatively.
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