Academic literature on the topic 'Chua circuit'
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Journal articles on the topic "Chua circuit"
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Chua, Leon. "Chua circuit." Scholarpedia 2, no. 10 (2007): 1488. http://dx.doi.org/10.4249/scholarpedia.1488.
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Zhang, Xiufang, Chunni Wang, Jun Ma, and Guodong Ren. "Control and synchronization in nonlinear circuits by using a thermistor." Modern Physics Letters B 34, no. 25 (June 3, 2020): 2050267. http://dx.doi.org/10.1142/s021798492050267x.
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The survival and occurrence of chaos are much dependent on the intrinsic nonlinearity and parameters region for deterministic nonlinear systems, which are often represented by ordinary differential equations and maps. When nonlinear circuits are mapped into dimensional dynamical systems for further nonlinear analysis, the physical parameters of electric components, e.g. capacitor, inductor, resistance, memristor, can also be replaced by dynamical parameters for possible adjustment. Slight change for some bifurcation parameters can induce distinct mode transition and dynamics change in the chaotic systems only when the parameter is adjustable and controllable. In this paper, a thermistor is included into the chaotic Chua circuit and the temperature effect is considered by investigating the mode transition in oscillation and the dependence of Hamilton energy on parameters setting in thermistor. Furthermore, the temperature of thermistor is adjusted for finding possible synchronization between two chaotic Chua circuits connected by a thermistor. When the coupling channel via thermistor connection is activated, two identical Chua circuits (periodical or chaotic oscillation) can reach complete synchronization. In particular, two periodical Chua circuits can be coupled to present chaotic synchronization by taming parameters in thermistor of coupling channel. However, phase synchronization is reached while complete synchronization becomes difficult when the coupling channel is activated to coupling a periodical Chua circuit and a chaotic Chua circuit. It can give guidance for further control of firing behaviors in neural circuits when the thermistor can capture the heat effectively.
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BROWN, RAY. "FROM THE CHUA CIRCUIT TO THE GENERALIZED CHUA MAP." Journal of Circuits, Systems and Computers 03, no. 01 (March 1993): 11–32. http://dx.doi.org/10.1142/s0218126693000034.
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We analytically derive a one-dimensional map from an ODE which produces a double scroll very similar to the Chua double scroll. Our analysis leads us to suggest a generalization of the Chua circuit to an n-dimensional system of ODEs that we will call the generalized Chua equations. The third order system of ODEs in this class contains the Chua equations as a special case. Parallel to the generalized Chua equations we define the generalized Chua maps. An important feature of these equations and maps is that the source of their nonlinearity is a sigmoid function, and functions very similar in their properties to the sigmoid function. We show that this class of equations contains examples of maps that reproduce the Lorenz and Rössler dynamics. We suggest that a general theory of these equations and maps, and their relationship to one-dimensional maps, is possible. A benefit of our analysis shows that the dynamics of the maps of Rössler, Chua, and Lorenz maps can be traced to a common set of building blocks, and we conclude that the Chua map is the simplest of the three maps and therefore understanding the complexity in the Chua map provides a foundation for understanding chaos in a large class of n-dimensional equations that includes the maps of Rössler and Lorenz.
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Wang, Chunni, Zhao Yao, Wenkang Xu, and Guodong Ren. "Phase synchronization between nonlinear circuits by capturing electromagnetic field energy." Modern Physics Letters B 34, no. 29 (July 14, 2020): 2050323. http://dx.doi.org/10.1142/s0217984920503236.
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Smart nonlinear circuits can be tamed to reproduce the main dynamical properties in neural activities and thus neural circuits are built to estimate the occurrence of multiple modes in electric activities. In the presence of electromagnetic radiation, the cardiac tissue, brain and neural circuits are influenced because field energy is injected and captured when induction field and current are generated in the media and system. In this paper, an isolated Chua circuit is exposed to external electromagnetic field and energy capturing is estimated for nonlinear analysis from physical viewpoint. Furthermore, two Chua circuits without direct variable coupling are exposed to the same electromagnetic field for energy capturing. Periodical and noise-like radiations are imposed on the Chua circuits which can capture the magnetic field energy via the induction coil. It is found that the two Chua circuits (periodical or chaotic) can reach phase synchronization and phase lock in the presence of periodical radiation. On the other hand, noise-like radiation can realize complete synchronization between two chaotic Chua circuits while phase lock occurs between two Chua circuits in periodical oscillation. It gives some important clues to control the collective behaviors of neural activities under external field.
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BILOTTA, ELEONORA, PIETRO PANTANO, and FAUSTO STRANGES. "A GALLERY OF CHUA ATTRACTORS: PART II." International Journal of Bifurcation and Chaos 17, no. 02 (February 2007): 293–380. http://dx.doi.org/10.1142/s0218127407017343.
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Chua's circuit is a physical system which can be used to investigate chaotic processes. One of its identifying features is the ability to produce a huge variety of strange attractors, each with its own characteristic form, size and model. These characteristics extend to a range of different systems derived from the original circuit.In the first paper A Gallery of Chua's Attractors. Part I, we presented physical circuits and some generalizations based on Chua's oscillator, together with techniques for building the circuit and a summary description of its chaotic behavior.In this second part of our work, we present an overview of forms which can only be produced by the physical circuit, using novel techniques of scientific visualization to explore, discover, analyze and validate our large collection of data. Starting with cases already known in the literature, we show that the circuit can produce an infinite set of three-dimensional patterns. A small sample is included in our paper. More specifically, we present 195 strange attractors generated by the circuit. For each attractor we provide three-dimensional images, time series and FFTs. Finally, we provide Lyapunov exponents for a subset of "base attractors".
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Ahamed, A. Ishaq, and M. Lakshmanan. "Sliding Bifurcations in the Memristive Murali–Lakshmanan–Chua Circuit and the Memristive Driven Chua Oscillator." International Journal of Bifurcation and Chaos 30, no. 14 (November 2020): 2050214. http://dx.doi.org/10.1142/s0218127420502144.
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In this paper, we report the occurrence of sliding bifurcations admitted by the memristive Murali–Lakshmanan–Chua circuit [Ishaq & Lakshmanan, 2013] and the memristive driven Chua oscillator [Ishaq et al., 2011]. Both of these circuits have a flux-controlled active memristor designed by the authors in 2011, as their nonlinear element. The three-segment piecewise-linear characteristic of this memristor bestows on the circuits two discontinuity boundaries, dividing their phase spaces into three subregions. For proper choice of parameters, these circuits take on a degree of smoothness equal to one at each of their two discontinuities, thereby causing them to behave as Filippov systems. Sliding bifurcations, which are characteristic of Filippov systems, arise when the periodic orbits in each of the subregions, interact with the discontinuity boundaries, giving rise to many interesting dynamical phenomena. The numerical simulations are carried out after incorporating proper zero time discontinuity mapping (ZDM) corrections. These are found to agree well with the experimental observations which we report here appropriately.
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BORRESEN, J., and S. LYNCH. "FURTHER INVESTIGATION OF HYSTERESIS IN CHUA'S CIRCUIT." International Journal of Bifurcation and Chaos 12, no. 01 (January 2002): 129–34. http://dx.doi.org/10.1142/s021812740200422x.
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For a system to display bistable behavior (or hysteresis), it is well known that there needs to be a nonlinear component and a feedback mechanism. In the Chua circuit, nonlinearity is supplied by the Chua diode (nonlinear resistor) and in the physical medium, feedback would be inherently present, however, with standard computer models this feedback is omitted. Using Poincaré first return maps, bifurcations for a varying parameter in the Chua circuit equations are investigated for both increasing and decreasing parameter values. Evidence for the existence of a small bistable region is shown and numerical methods are applied to determine the behavior of the solutions within this bistable region.
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KILIÇ, RECAI. "EXPERIMENTAL MODIFICATIONS OF VOA-BASED AUTONOMOUS AND NONAUTONOMOUS CHUA'S CIRCUITS FOR HIGHER DIMENSIONAL OPERATION." International Journal of Bifurcation and Chaos 16, no. 09 (September 2006): 2649–58. http://dx.doi.org/10.1142/s0218127406016318.
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In order to operate in higher dimensional form of autonomous and nonautonomous Chua's circuits keeping their original chaotic behaviors, we have experimentally modified VOA (Voltage Mode Operational Amplifier)-based autonomous Chua's circuit and nonautonomous MLC [Murali–Lakshmanan–Chua] circuit by using a simple experimental method. After introducing this experimental method, we will present PSpice simulation and experimental results of modified high dimensional autonomous and nonautonomous Chua's circuits.
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YU, SIMIN, WALLACE K. S. TANG, and G. CHEN. "GENERATION OF n × m-SCROLL ATTRACTORS UNDER A CHUA-CIRCUIT FRAMEWORK." International Journal of Bifurcation and Chaos 17, no. 11 (November 2007): 3951–64. http://dx.doi.org/10.1142/s0218127407019809.
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In this paper, the generation of n × m-scroll attractors under a Chua-circuit framework is presented. By using a sawtooth function, f1(x), and a staircase function, f2(y), n × m-scroll attractors can be generated and observed from a third-order circuit. Its dynamical behaviors are investigated by means of theoretical analysis as well as numerical simulation. Moreover, two electronic circuits are designed for its realization, and experimental observations of n × m-scroll attractors based on Chua's circuit are reported, for the first time in the literature.
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BROWN, RAY. "GENERALIZATIONS OF THE CHUA EQUATIONS." International Journal of Bifurcation and Chaos 02, no. 04 (December 1992): 889–909. http://dx.doi.org/10.1142/s0218127492000513.
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In this paper we present two generalizations of the equations governing Chua’s circuit. In order to obtain the first generalization we simplify Chua’s equations by replacing the piecewise-linear term with a signum function. The resulting simplified system produces a double scroll similar to the one observed experimentally in Chua’s circuit. What is significant about this simplified system is that it can be reduced to what we shall call a two-dimensional single scroll, and from the two-dimensional single scroll we are able to derive a one-dimensional map. This entire derivation is carried out analytically, in contrast to the one-dimensional map analysis that has been carried out for the Lorenz equations which is based on axioms. After we have carried out our analysis for this simplified version of Chua’s equations, we use these equations as a guide to the construction of the first generalization to be presented in this paper. We call this a type-I generalization of Chua’s equations. The generalization consists in using a two-dimensional autonomous flow as a component in a three-dimensional autonomous flow in such a way that the resulting equations will have double scroll attractors similar to those observed experimentally in Chua’s circuit. The value of this generalization is that: (1) it provides a building block approach to the construction of chaotic circuits from simpler two-dimensional components which are not chaotic by themselves. In so doing it provides an insight into how chaotic systems can be built up from simple nonchaotic parts; (2) it illustrates a precise relationship between three-dimensional flows and one-dimensional maps. Of particular significance in this regard is a recent paper of Misiurewicz [1993], which analytically connects the two-dimensional single scroll to the class of unimodal maps, thus providing a framework within which a theory linking unimodal maps to three-dimensional flows may be possible. The second generalization is suggested by considering three-dimensional flows whose only nonlinearities are sigmoid, sgn, or piecewise-linear functions. Clearly, such flows are a generalization of the Chua equations. We call these equations type-II generalization Chua equations. The significance of this direction of investigation is that attractors similar to the Lorenz and Rössler attractors can be produced from type-II generalized Chua equations in a building block approach using only piecewise-linear vector fields. As a result we have a method of producing the Lorenz and Rössler dynamics in a circuit without the use of multipliers. This suggests that the type-II generalized Chua equations are in some sense fundamental in that the dynamics of the three most important autonomous three-dimensional differential equations producing chaos are seen as variations of a single class of equations whose nonlinearities are generalizations of the Chua diode.
Dissertations / Theses on the topic "Chua circuit"
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Maranhão, Dariel Mazzoni. "Estudo topológico de órbitas periódicas no circuito experimental de Chua." Universidade de São Paulo, 2006. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-24032007-174511/.
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Estudamos o comportamento dinâmico de séries temporais experimentais obtidas de um circuito de Chua quando dois parâmetros de controle, $Delta R_1$ e $Delta R_2$, são variados.Investigamos os comportamentos caótico e periódico, analisando as séries temporais ao redor e no interior de duas janelas periódicas presentes no espaço de parâmetros $(Delta R_1,Delta R_2)$ do circuito. Na vizinhança da janela de período três, analisamos como a dinâmica simbólica se altera quando construída em diferentes seções de Poincaré de um mesmo atrator, e investigamos a dimensão dos mapas de retorno, uni ou bidimensional, para diferentes atratores caóticos presentes nessa região do espaço de parâmetros. Ainda nessa vizinhança, empregamos técnicas de caracterização topológica para confirmar a existência de fibras caóticas, que são curvas de codimensão um no espaço de parâmetros onde as propriedades caóticas dos atratores são preservadas.Ao redor da janela de período quatro, investigamos a transição entre os três comportamentos caóticos para os quais construímos os respectivos moldes topológicos. Propusemos também um molde topológico para o regime caótico após a crise por fusão ocorrer no circuito. Finalizando, investigamos as bifurcações e a estrutura topológica das órbitas periódicas que formam as janelas de período três e de período quatro, construindo um espaço de parâmetros topológico, baseado em um mapa bi-modal, para descrever as duas janela periódicas.We have studied the dynamical behavior of experimental time series obtained from a Chua's circuit by variation of two parameter control, $Delta R_1$ and $Delta R_2$. We investigated the chaotic and periodic behaviors of the circuit, analyzing temporal series around and inside of two periodic windows in the two-parameter space $(Delta R_1,Delta R_2)$. In the period-three window neighborhood, we analyzed how the symbolic dynamics changes when it is built by different Poincaré sections of an attractor, and we studied the dimension of return map, one- or two-dimensional, for many chaotic attractors in this region of the parameter space. In this neighborhood, we also applied topological techniques to confirm the existence of chaotic fibers: codimension one curves where the chaotic properties of the attractors remain unchanged in the two-parameter space.Around the period-four window, we investigated, by template analysis, the transition between three chaotic attractors found in the Chua's circuit. We proposed a template for chaotic regime of the circuit after merge-crisis. Finally, we investigated the bifurcations and topological structure of periodic orbits in period-three and period-four windows and also proposed a topological parameter space, based in a bimodal map model, that describe these two periodic windows.
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HAMRI, NASR-EDDINE. "Continuite de la demi application de poincare dans les equations du circuit de chua." Nice, 1994. http://www.theses.fr/1994NICE4798.
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Nous presentons un circuit electronique simple decrit par des equations equivalentes a un systeme de trois equations differentielles ordinaires, lineaire par morceaux. En depit de la simplicite des equations, les demi-applications de poincare ne sont pas connues explicitement, et il reste difficile de donner des resultats mathematiques exacts sur la nature des oscillations de ce circuit. Pour etudier et comprendre le comportement des solutions d'un systeme dynamique comme celui que nous considerons comme modele, il suffit d'etudier la structure interne de son confineur principal s'il existe. Dans le cas des equations qui modelisent la dynamique du circuit de chua dont l'application de poincare est de dimension 2, l'existence d'un confineur de dimension 3 a pu etre prouvee dans certain cas, ce qui exige des courbes comme frontieres pour les confineurs. A cet effet, nous utilisons les demi-applications de poincare definies localement. Nous etudions la continuite d'une demi-application qui permettra l'utilisation de la dynamique symbolique liee aux droites isochroniques. Nous montrons que la discontinuite de la demi-application de poincare est liee a l'intersection des droites isochroniques a l'interieur de la partie attractante pour le flot. Nous abordons aussi quelques aspects sur les applications du modele dans les domaines de la synchronisation et du controle du chaos
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Rujzl, Miroslav. "Analýza a obvodové realizace speciálních chaotických systémů." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2021. http://www.nusl.cz/ntk/nusl-442418.
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This master‘s thesis deals with analysis of electronic dynamical systems exhibiting chaotic solution. In introduction, some basic concepts for better understanding of dynamical systems are explained. After introduction, current knowledge from the world of circuits exhibiting chaotic solutions are discussed. The best-known chaotic systems are analyzed numerically in Matlab software. Numerical analysis and experimental verification were demonstrated at C class transistor amplifier, which confirmed the chaotic behavior and generation of a strange attractor.
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Bonet, Dalmau Jordi. "Análisis del régimen permanente y la estabilidad de circuitos no lineales con parámetros distribuidos mediante técnicas de tiempo discreto." Doctoral thesis, Universitat Politècnica de Catalunya, 1999. http://hdl.handle.net/10803/6889.
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En esta tesis se ha abordado el problema de la determinación directa del régimen permanente de circuitos no lineales autónomos con parámetros distribuidos en el dominio temporal. Con la obtención de las ecuaciones de equilibrio en el dominio transformado de Laplace, es posible escribir directamente el sistema de ecuaciones discretizado en el dominio temporal, donde las incógnitas son el periodo de oscilación y las muestras de las variables de control. Así, toda variable genérica V(s) es transformada en un vector de muestras equiespaciadas de v(t), y cada uno de los operadores, derivada y retardo, en una matriz circulante. La formulación obtenida es tal que posibilita el posterior desarrollo analítico de la sensibilidad del sistema de ecuaciones discretizado respecto al periodo de oscilación y las muestras de las variables de control, permitiendo una eficaz resolución del sistema de ecuaciones utilizando métodos globalmente convergentes basados en modificaciones del método de Newton. Además, con el método de análisis propuesto, es posible reconvertir un problema de optimización en un problema de análisis y, en consecuencia, de menor complejidad. La utilización de los aproximantes de Padé multipunto, para aproximar una línea de transmisión RLCG con elementos de parámetros concentrados y una línea de transmisión ideal, permite extender el método propuesto a los circuitos que incorporan líneas RLCG.Una vez determinadas las soluciones en régimen permanente, el siguiente problema a abordar es el estudio de la estabilidad de estas soluciones, utilizándose los resultados de este estudio para detectar bifurcaciones de Hopf, de desdoblamiento de órbitas y puntos límite. En esta tesis se describe una técnica que permite seguir a) la rama que continua tras la aparición de un punto límite y b) la rama de periodo doble existente en una bifurcación de desdoblamiento de órbitas, como se comprueba sobre el circuito de Chua retardado (TDCC),
Otra aportación de esta tesis, desarrollada íntegramente en el plano teórico, ha consistido en estrechar los lazos existentes entre el estudio de la estabilidad en el dominio temporal y el dominio frecuencial. El punto de partida se encuentra en la obtención de una transformación que permite trasladar cualquier formulación de análisis del dominio frecuencial al temporal y viceversa. La extensión de estos vínculos al estudio de la estabilidad deriva en la obtención de importantes resultados. Destaca, entre éstos, la obtención de la formulación de estabilidad utilizada por el método de balance armónico (HB), partiendo de un estudio de la estabilidad realizado en el dominio temporal. Estos resultados se complementan con los obtenidos por otros autores que, partiendo de una formulación en el dominio temporal con variables de estado, obtienen una formulación en el dominio frecuencial.
Con la finalidad de no avanzar en el vacío, las ideas que aparecen en esta tesis han sido siempre contrastadas, en algunos casos por más de una vía. Así, el circuito de Van der Pol se analiza con el método de HB y con el método propuesto utilizando tres formulaciones distintas. El estudio de la estabilidad de los puntos de equilibrio del TDCC se contrasta con resultados analíticos. La determinación de las regiones de funcionamiento del circuito de Van der Pol excitado y la construcción de su curva solución se comparan con los resultados obtenidos usando HB. Los resultados de análisis del TDCC con línea RLCG son contrastados con los resultados obtenidos utilizando métodos de integración. Finalmente, se realiza una validación experimental del oscilador con línea de transmisión, sobre el cual se resuelve un problema de análisis y otro de optimización.
This thesis has tackled the problem of the direct determination of the steady state analysis of autonomous circuits with transmission lines and generic nonlinear elements. With the equilibrium equations obtained in the Laplace transformed domain, it is possible to directly write the discretized system of equations in the temporal domain where the unknowns to determine are the samples of the control variables, directly in the steady state, along with the oscillation period. Thus, every generic variable V(s) is converted into a vector of equally spaced samples of v(t) and each one of the operators, derivative and delay, into a circulant matrix. The formulation obtained is such that makes it possible the subsequent analytic development of the sensibility of the system of equations discretized with respect to the oscillation period and the samples of the control variables, allowing to solve the system of equations effectively using globally convergent techniques based on modifications of the Newton method. Moreover, with the analysis method suggested here, it is possible to turn a problem of optimization into a problem of analysis and, subsequently, of a lesser complexity. Besides, the use of the multipoint Padé approximants, to approximate an RLCG transmission line with lumped elements and an ideal transmission line, makes it possible to extend the suggested method to the circuits that include RLCG transmission lines.
Once the steady state solutions have been determined, the next problem to deal with is the study of the stability of these solutions. The results of this study are used to detect Hopf bifurcations, period-doubling bifurcations and limit points. In this thesis a technique is described which allows us to follow a) the branch that follows after the appearance of a limit point and b) the branch of double period that exists in a period-doubling bifurcation point, as it can be proved in the time delayed Chua's circuit (TDCC).
Another contribution of this thesis, totally developed at a theoretical level, has consisted in strengthening the existing bonds between the study of the stability both in the temporal and in the frequency domain. The starting point is a transformation that makes it possible to transfer any analysis formulation from the frequency domain to the temporal one and vice versa. The extension of these links to the study of the stability leads to important results. It stands out, among them, the obtained formulation of stability used by the harmonic balance (HB) method, starting from a stability study made in the temporal domain. These results complement each other with those obtained by other authors who, starting from a formulation in the temporal domain with state variables, obtain a formulation in the frequency domain.
With the purpose of validating the ideas that appear in this thesis, these have always been contrasted, in some cases in more than one way. Thus, the Van der Pol oscillator is analyzed with the HB method and with the method suggested here using three different formulations. The study of the stability of the equilibrium points of the TDCC is contrasted with analytic results. The determination of the working regions of the excited Van der Pol oscillator and the construction of its solution curve is compared with the results obtained using HB. The results of the analysis of the TDCC with RLCG line are contrasted with those obtained using integration techniques. Finally, an experimental validation of an oscillator with transmission line is made, in which a problem of analysis and another one of optimization are solved.
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Baptista, Murilo da Silva. "Perturbando Sistemas Não-Lineares, uma Abordagem do Controle de Caos." Universidade de São Paulo, 1996. http://www.teses.usp.br/teses/disponiveis/43/43131/tde-13122007-093342/.
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Inicialmente, consideramos o mapa Logístico com os vários fenômenos nele presentes, para depois, ao perturbarmos esse mapa, adicionando periodicamente um termo de amplitude constante, identificarmos os novos fenômenos e as alterações que a introdução da perturbação faz aparecer. Apresentamos o circuito eletrônico de Matsumoto e, em seguida, o consideramos em um regime caótico perturbado por uma tensão elétrica senoidal externa. A introdução desta perturbação faz o circuito permanecer caótico, tornar-se periódico ou quasi-periódico no toro de duas frequências. Aplicamos diversos métodos de controle de caos a três sistemas (mapa Logístico, mapa de Hénon e circuito de Matsumoto). Para a estabilização de uma órbita periódica, consideramos os métodos de Ott-Grebogi-Yorke (OGY), de Romeiras, de Pyragas, de Sinha, de Singer e de H¨ubbler. Para o direcionamento da trajetória para um ponto de equilíbrio, usamos o método de Sinha. Para a transferência da trajetória para um dos atratores coexistentes no sistema de Matsumoto, usamos o método de Jackson-H¨ubbler (OPCL). Usando um conjunto de pertubações constantes em um parâmetro previamente escolhido, mostramos como é possével dirigir rapidamente uma trajetória, de qualquer um dos três sistemas considerados nesta tese, para um determinado alvo. Além disso, é mostrado como esse método pode ser aplicado experimentalmente.Initially, we consider the Logistic map with its many non-linear phenomena. Then, we use this knowledge to discern new phenomena that shall appear when the map is perturbed, that is the Logistic map perturbed by a periodic and constant term. The Matsumoto\'s circuit is presented and, after we set this circuit to behave chaotically, we perturb it with a sinoidal wave, characterized by its frequency and amplitude. This perturbation is responsible for the appearence of a quasi-periodic and periodic oscillations, or the maintenance of chaos. We presented and applied many methods for controlling chaotic oscillations in three systems (the Logistic and Henon maps, and the Matsumoto\'s circuit), showing many ways for stabilizing a periodic orbit, using the methods of Ott-Grebogi-York (OGY), Romeiras, Singer, Sinhas and Huebbler. For targeting the trajectory to a equilibrium point, the Sinha\'s method was used. To transfer the system trajectory from one to another of the coexisting attractors presented in the Matsumoto\'s circuit, we use the Jackson-Huebbler (OPCL) method. Using a set of constant perturbations, in a previously chosen parameter, we showed how we can rapidly direct a trajectory of any of the considered three systems to a aimed target. Besides, it is shown how this method can be experimentally applied.
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SOUSA, Francisco Felipe Gomes de. "Análise dos espaços de parâmetros do circuito de Chua experimental." reponame:Repositório Institucional da UNIFEI, 2016. http://repositorio.unifei.edu.br:8080/xmlui/handle/123456789/514.
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Neste trabalho, foram obtidos experimentalmente os espaços de parâmetros bidimensionais da periodicidade e do maior expoente de Lyapunov para o circuito de Chua, usando as medidas de séries temporais para diferentes valores das resistências rL em série com o indutor e R ligada aos dois capacitores. Este circuito apresenta o comportamento de um material semicondutor com condutividade diferencial negativa que lembra a forma da letra N (NNDC) acoplado a um circuito tanque. Quatro potenciômetros digitais com 1024 passos de 0,100 Ω, 0, 200 Ω e 1,000 Ω foram construídos para modificar os valores destes parâmetros. A aquisição de dados e controle dos potenciômetros digitais foram feitas através de um programa desenvolvido em Labview® e a análise de dados e apresentação dos resultados com scripts em PYTHON. Os resultados obtidos foram comparados com simulações feitas em FORTRAN que confirmaram a presença de cascatas de adição de período, janelas periódicas, rotas de adição de períodos impares, coexistência de atratores e um hub de periodicidade. Confirmando a eficácia dos usos dos potenciômetros digitais como alternativa para variar os parâmetros resistivos de sistemas dinâmicos elétricos.
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Prebianca, Flavio. "Estudo de um circuito de Chua com realimentação tipo seno." Universidade do Estado de Santa Catarina, 2014. http://tede.udesc.br/handle/handle/1987.
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The Chua s circuit is an electronic oscillator that has a non-linearity coupled to an LC oscillator, enabling the study of experimental chaos. Using the method of feedback with sine function of the voltage from C1 capacitor, indirectly alters the nonlinear curve of the circuit, with new operation points allowing the emergence of four scroll attractors. A consequence of this feedback is the emergence of a new chaotic region in the parameter space. We present here a qualitative numerical study simulated via MULTISIM/SPICE. It also presents the study by fourth order Runge-Kutta numerical integration for the construction of the parameter space of the largest Lyapunov exponent and bifurcation diagram. It explores the crisis region in the numerical study and show the experimental attractors in this phenomenon. We seek to compare the crisis phenomenon relating the number of visits that system is in the regions +V1 and −V1.
O circuito de Chua é um oscilador eletrônico que possui uma não-linearidade acoplada a um oscilador LC, viabilizando o estudo de caos experimental. Utilizando o método de realimentação por função senoidal da tensão do capacitor C1, altera-se indiretamente a curva não linear do circuito, com novos pontos de operação do oscilador, possibilitando o surgimento de atratores de quatro rolos. Uma consequência desta realimentação ´e o surgimento de uma nova região de caos no espaço de parâmetros. Apresenta-se neste trabalho, o estudo numérico qualitativo simulado via MULTISIM/SPICE. Também apresenta o estudo por integração numérica pelo método Runge-Kutta de quarta ordem, para a construção do espaço de parâmetros do maior expoente de Lyapunov e diagrama de bifurcação. Explora-se a região de crise no estudo numérico e mostra-se atratores experimentais em tal fenômeno. Buscamos comparar o fenômeno de crise relacionando o numero de visitas que o atrator faz nas regiões +V1 e −V1.
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SOUZA, João Paulo Araújo. "Espaço de parâmetros de dois circuitos de Chua sincronizados." reponame:Repositório Institucional da UNIFEI, 2018. http://repositorio.unifei.edu.br/xmlui/handle/123456789/1085.
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Nesta dissertação são apresentados os resultados do estudo do espaço de parâmetros da periodicidade experimental, expoente de Lyapunov simulado e experimental e faixa de resistência no qual dois circuitos de Chua se sincronizam. A simulação foi realizada através do software Fortran, no qual contribui para as análises dos resultados experimentais. Com o desenvolvimento do programa no software Labview® foram obtidas séries temporais que descrevem o sistema experimental. Para montagem experimental foram construídos dois circuitos de Chua e cinco potenciômetros. Os potenciômetros são os parâmetros de controle do nosso sistema definido como R e rl, no qual R tem variação de sua resistência no passo de 1Ω e rl no passo de 0,1Ω. Para análise dos resultados experimentais, foram desenvolvidos programas em Labview® e scripts em Python que fizeram análise das series temporais no qual foram obtidos resultados como periodicidade, maior expoente de Lyapunov e como simulação obtivemos, dimensão de Kaplan-Yorke e entropia de Kolmogorov-Sinai. Os resultados das analises foram representados na forma de espaço de parâmetros. Medições de sincronismo para dois circuitos de Chua acoplados foram realizadas para identificar a intensidade do acoplamento em função da resistência de acoplamento. Simulações do espaço de parâmetros, numa condição de acoplamento com travamento de fase foram utilizadas permitindo identificar as mesmas estruturas observadas para circuitos desacoplados.
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Santos, Elinei Pinto dos. "Bifurcações, controle e sincronização do caos nos circuitos de Matsumoto-Chua." Universidade de São Paulo, 2001. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-04122013-105609/.
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Neste trabalho utilizamos técnicas de controle e sincronização de sistemas caóticos, visando o uso delas para comunicação com caos. Aplicamos tais técnicas no circuito elétrico de Matsumoto-Chua. Inicialmente, mostramos a sensibilidade dos atratores deste circuito quando variamos os seus parâmetros. Determinamos as suas bacias de atração. Através da análise biespectral, verificamos que o acoplamento quadrático é alto para o atrator tipo Rössler, e quase nulo para o atrator Espiral-Dupla. Para a caracterização global do circuito, apresentamos diagramas, no espaço de parâmetros, com os valores dos expoentes de Lyapunov ou autocorrelação. A seguir estudamos esse circuito com uma perturbação senoidal. Com isto, identificamos novos cenários para a transição para o caos a partir da quase periodicidade. Duas destas transições foram identificados pela primeira vez nesse circuito. Aplicamos ao circuito cinco métodos de controle de caos: supressão de caos por sincronização de freqüências, controle de órbitas periódicas instáveis pelos métodos OGY e de realitnentação , estabilização no ponto ele equilíbrio (método de Hwang), migração e arraste (método OPCL). Finalmente, consideramos dois circuitos de Matsumo-Chua acoplados e determinamos as suas bacias de sincronização. Mostramos que a sincronização dos circuitos acoplados pode não depender das condições iniciais (fronteira das bacias contínua) ou ser extremamente sensível às condições iniciais (fronteira elas bacias elo tipo crivada ou intercrivada).In this work we use control and synchronization of chaos techniques aiming their implementation in communicating with chaos. These techniques are applied into the electric circuit of Matsumoto-Chua. Initialty, we show the sensibility of the attractors under parameter variations. We determine the attractor basin of attractions. Through the bi-spectral analysis, we verify that the quadratic coupling is high for the Rössler-type attractor, and almost null for the Double-Scroll attractor. For the global charactcrization of this system, we show parameter diagrams of the Lyapunov exponents or auto-correlation. We also study this circuit under a sinusoidal perturbation. In this configuration, we identify new scenario for the transition to chaos through quasi-periodicity. Two of these transitions are identified by us for the first time in this perturbed circuit. We apply five control of chaos techniques: chaos suppression by frequency synchronization, control of unstable periodic orbits by the OGY and feed-back methods, stabilization of the equilibrium points (Hwang method), migration and entrainment (OPCL method). Finally, we consider two acoupled Matsumoto-Chua\'s circuits and determine their synchronization basins. We show that the synchronization in these coupled circuits may not depend on the initial conditions (continuous synchronization basin boundary) or may depend extremely on the initial conditions (riddled or intermingled synchronization basin boundaries).
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Zhu, Ning. "Advances in Non-Foster Circuit Augmented, Broad Bandwidth, Metamaterial-Inspired, Electrically Small Antennas." International Foundation for Telemetering, 2012. http://hdl.handle.net/10150/581683.
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ITC/USA 2012 Conference Proceedings / The Forty-Eighth Annual International Telemetering Conference and Technical Exhibition / October 22-25, 2012 / Town and Country Resort & Convention Center, San Diego, CaliforniaThere are always some intrinsic tradeoffs among the performance characteristics: radiation efficiency, directivity, and bandwidth, of electrically small antennas (ESAs). A non-Foster enhanced, broad bandwidth, metamaterial-inspired, electrically small, Egyptian axe dipole (EAD) antenna has been successfully designed and measured to overcome two of these restrictions. By incorporating a non-Foster circuit internally in the near-field resonant parasitic (NFRP) element, the bandwidth of the resulting electrically small antenna was enhanced significantly. The measured results show that the 10 dB bandwidth (BW10dB) of the non-Foster circuit-augmented EAD antenna is more than 6 times the original BW10dB value of the corresponding passive EAD antenna.
Books on the topic "Chua circuit"
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Chuan gan qi ying yong ji dian lu she ji. Beijing Shi: Hua xue gong ye chu ban she, 2008.
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Chuan gan qi ying yong ji dian lu she ji. Beijing Shi: Hua xue gong ye chu ban she, 2008.
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Zhang Zhongmou de ce lüe chuan qi. Taibei Shi: Tian xia za zhi, 1998.
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Sirakoulis, Georgios Ch, and Ioannis Vourkas. Memristor-Based Nanoelectronic Computing Circuits and Architectures: Foreword by Leon Chua. Springer, 2015.
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Chen, G., Andrew Adamatzky, and Leon O. Chua. Chaos, CNN, Memristors and Beyond: A Festschrift for Leon Chua. World Scientific Publishing Co Pte Ltd, 2013.
Find full textBook chapters on the topic "Chua circuit"
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Leonov, Gennady A., and Nikolay V. Kuznetsov. "Analytical-Numerical Methods for Hidden Attractors’ Localization: The 16th Hilbert Problem, Aizerman and Kalman Conjectures, and Chua Circuits." In Computational Methods in Applied Sciences, 41–64. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-5288-7_3.
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"THE PHYSICAL CIRCUIT." In A Gallery of Chua Attractors, 61–148. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812790637_0002.
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BROWN, RAY. "FROM THE CHUA CIRCUIT TO THE GENERALIZED CHUA MAP." In Chua's Circuit: A Paradigm for Chaos, 629–50. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789812798855_0034.
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MISIUREWICZ, MICHAŁ. "UNIMODAL INTERVAL MAPS OBTAINED FROM THE MODIFIED CHUA EQUATIONS." In Chua's Circuit: A Paradigm for Chaos, 651–68. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789812798855_0035.
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Dana, Syamal Kumar, and Satyabrata Chakraborty. "Experimental Evidences of Shil'nikov Chaos and Mixed-mode Oscillation in Chua Circuit." In Chaos Synchronization and Cryptography for Secure Communications, 91–104. IGI Global, 2011. http://dx.doi.org/10.4018/978-1-61520-737-4.ch005.
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Experimental evidences of Shil’nikov type homoclinic chaos and mixed mode oscillations are presented in asymmetry-induced Chua‘s oscillator. The asymmetry plays a crucial role in the related homoclinic bifurcations. The asymmetry is introduced in the circuit by forcing a DC voltage. The authors observed transition from large amplitude limit cycle to homoclinic chaos via a sequence of mixed-mode oscillations interspersed by chaotic states by tuning a control parameter.
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Boutat-Baddas, L., J. Barbot, and R. Tauleigne. "Implementation of the Chua‚Äôs Circuit and its Application in the Data Transmission." In Chaos in Automatic Control, 503–25. CRC Press, 2005. http://dx.doi.org/10.1201/9781420027853.ch14.
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Keats, Jonathon. "Memristor." In Virtual Words. Oxford University Press, 2010. http://dx.doi.org/10.1093/oso/9780195398540.003.0014.
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The capacitor was discovered in 1745 by Ewald Georg von Kleist, whose encounter with a generator and a jar of water shocked him so severely that he declared himself unwilling to repeat the experience “for the kingdom of France.” The resistor announced itself to mankind somewhat less dramatically in 1827, followed by the inductor in 1831. For the next 140 years these three components were considered the basic elements of electronics. Each accomplished what the others could not, even in combination, and together they gave engineers rudimentary control over electromagnetism. The capacitor linked charge and current, the resistor, current and voltage, and the inductor, current and flux. Later innovations, most notably the invention of transistors in 1947, would vastly expand the capability of electronics and even more incredibly stretch our expectations, yet everyone remained satisfied with the three old “passive” elements. If any more existed there simply was no need to find them. Then along came a young engineer named Leon Chua, who, unusual for someone in his profession, had an Aristotelian turn of mind. Instead of asking himself what could be done with capacitors and resistors and inductors, he sought to define what they were. His definitions, expressed in abstract terms of charge and current and voltage and flux, suggested to him an incomplete pattern, like a crossword puzzle with all but one word filled in. In 1971 he predicted the existence of a missing link between flux and charge. He gave it a name. He called his component a memristor . Still, it was only a placeholder, since nobody had ever seen one or cared about manufacturing them. His mathematical reasoning was elegant, acknowledged those who bothered to follow it, but engineers were much more excited by his 1983 invention of a simple circuit that behaved chaotically (in the formal mathematical sense), with obvious applications in computing and security. The circuit was named in his honor, making him a very minor celebrity.
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Seely, Warren, Jakub Kucera, Urs Lott, Anthony Pavio, Charles Nelson, Mark Bloom, Alfy Riddle, Robert Newgard, Richard Snyder, and Robert Trew. "Circuits." In Electrical Engineering Handbook. CRC Press, 2000. http://dx.doi.org/10.1201/9781420036763.ch5a.
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Alain, Kammogne Soup Soup Tewa, and Fotsin Hilaire Bertrand. "Robust Control Methods for Finite Time Synchronization of Uncertain Nonlinear Systems." In Advances in Systems Analysis, Software Engineering, and High Performance Computing, 364–98. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-5788-4.ch015.
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This chapter addresses the dynamic analysis and two different control strategies for the synchronization of new topology of Colpitts oscillator submitted to uncertainties and external disturbances. The diagrams obtained reveal precisely spirals bifurcation and chaos when for a specific values of the system parameters. Based on the relevant control, the authors have controlled this striking phenomenon in the system. The first (control) deals with the sliding mode control (SMC) method. Some important aspects of the design and implementation are considered to reach a suitable controller for the applications. The second presents an adaptive robust tracking control strategy based on a modified polynomial observer which tends to follow exponentially the chaotic Colpitts circuits brought back to a topology of the Chua oscillator with perturbations. To highlight the contribution, they also present some simulation results with the purpose to compare the proposed method to the classical polynomial observer.
Conference papers on the topic "Chua circuit"
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Voliansky, Roman, Aleksander Sadovoi, and Yurii Shramko. "Chua Circuit with Several Voltage Sources." In 2018 International Scientific-Practical Conference Problems of Infocommunications. Science and Technology (PIC S&T). IEEE, 2018. http://dx.doi.org/10.1109/infocommst.2018.8632158.
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Jahed-Motlagh, Mohammad Reza, and Behnam Kia. "Chua Circuit Based Reconfigurable Computing System." In APCCAS 2006 - 2006 IEEE Asia Pacific Conference on Circuits and Systems. IEEE, 2006. http://dx.doi.org/10.1109/apccas.2006.342193.
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Dongping Wang, Hui Zhao, and Juebang Yu. "Chaos in memristor based Murali-Lakshmanan-Chua circuit." In 2009 International Conference on Communications, Circuits and Systems (ICCCAS). IEEE, 2009. http://dx.doi.org/10.1109/icccas.2009.5250352.
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Li, Ke, and Shu-Lin Wu. "A new synchronization controller of Chua chaotic circuit." In 2013 9th International Conference on Natural Computation (ICNC). IEEE, 2013. http://dx.doi.org/10.1109/icnc.2013.6818219.
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Haura Junior, Remei, Mauricio A. Ribeiro, Wagner Barth Lenz, José Manoel Balthazar, and Angelo Marcelo Tusset. "REVISTING THE BEHAVIOR OF BI-DIRECTIONAL COUPLED CHUA CIRCUIT." In 25th International Congress of Mechanical Engineering. ABCM, 2019. http://dx.doi.org/10.26678/abcm.cobem2019.cob2019-0364.
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Galias, Zbigniew. "Study of dynamical phenomena in the Muthuswamy-Chua circuit." In 2014 International Conference on Signals and Electronic Systems (ICSES). IEEE, 2014. http://dx.doi.org/10.1109/icses.2014.6948720.
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Vilasis-Cardona, Xavier, and Mireia Vinyoles-Serra. "Comparison between chua-yang and hyperbolic CNNs." In 2009 European Conference on Circuit Theory and Design (ECCTD 2009). IEEE, 2009. http://dx.doi.org/10.1109/ecctd.2009.5275040.
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Feki, Moez, and Ichraf Gammoudi. "Chaos in Chua circuit with fractional order low pass filter." In 2011 8th International Multi-Conference on Systems, Signals and Devices (SSD 2011). IEEE, 2011. http://dx.doi.org/10.1109/ssd.2011.5986785.
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Innocenti, Giacomo, Mauro Di Marco, Mauro Forti, and Alberto Tesi. "A controlled Murali-Lakshmanan-Chua memristor circuit to mimic neuron dynamics." In 2019 IEEE 58th Conference on Decision and Control (CDC). IEEE, 2019. http://dx.doi.org/10.1109/cdc40024.2019.9029330.
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Yuhuan Zhang, Zhenyou Zhang, and Yilong Lei. "Research on chaotic cryptosystem based on time delay feedback Chua circuit." In 2010 International Conference On Computer and Communication Technologies in Agriculture Engineering (CCTAE). IEEE, 2010. http://dx.doi.org/10.1109/cctae.2010.5544222.
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