Journal articles: '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.

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VOLOS, CHRISTOS K., IOANNIS M. KYPRIANIDIS, and IOANNIS N. STOUBOULOS. "AN UNIVERSAL PHENOMENON IN MUTUALLY COUPLED CHUA'S CIRCUIT FAMILY." Journal of Circuits, Systems and Computers 23, no. 02 (February 2014): 1450028. http://dx.doi.org/10.1142/s0218126614500285.

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This paper presents the universality of the coexistence of complete synchronization with the recently new proposed inverse π-lag synchronization, in the case of mutually coupled systems of Chua's circuit family. The phenomenon of multistability and the nature of this circuit family systems are the key-points which lead to the explanation of this coexistence. For the need of this work, the most representative circuit of this circuits' family, the Chua oscillator, is used. Simulation results confirm this universality in the class of Chua's circuit family.

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Balcerzak, M., A. Chudzik, and A. Stefanski. "Properties of generalized synchronization in smooth and non-smooth identical oscillators." European Physical Journal Special Topics 229, no. 12-13 (September 2020): 2151–65. http://dx.doi.org/10.1140/epjst/e2020-000010-5.

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Abstract This paper deals with the phenomenon of the GS only in the context of unidirectional connection between identical exciter and receivers. A special attention is focused on the properties of the GS in coupled non-smooth Chua circuits. The robustness of the synchronous state is analyzed in the presence of slight parameter mismatch. The analysis tools are transversal and response Lyapunov exponents and fractal dimension of the attractor. These studies show differences in the stability of synchronous states between smooth (Lorenz system) and non-smooth (Chua circuit) oscillators.

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Atan, Özkan. "Effects of Variable-Order Passive Circuit Element in Chua Circuit." Circuits, Systems, and Signal Processing 39, no. 5 (October 3, 2019): 2293–306. http://dx.doi.org/10.1007/s00034-019-01271-2.

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Garms, Marco A., Marco T. C. Andrade, and Iberê L. Caldas. "Fuzzy computational control for real Chua circuit." Chaos, Solitons & Fractals 39, no. 5 (March 2009): 2169–78. http://dx.doi.org/10.1016/j.chaos.2007.06.068.

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Gupta, M. K., and C. K. Yadav. "Jacobi stability analysis of modified Chua circuit system." International Journal of Geometric Methods in Modern Physics 14, no. 06 (May 4, 2017): 1750089. http://dx.doi.org/10.1142/s021988781750089x.

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In this paper, we analyze the nonlinear dynamics of the modified Chua circuit system from the viewpoint of Kosambi–Cartan–Chern (KCC) theory. We reformulate the modified Chua circuit system as a set of two second-order nonlinear differential equations and obtain five KCC-invariants which express the intrinsic geometric properties. The deviation tensor and its eigenvalues are obtained, that determine the stability of the system. We also obtain the condition for Jacobi stability and discuss the behavior of deviation vector near equilibrium points.

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Mannan, Zubaer Ibna, Hyuncheol Choi, and Hyongsuk Kim. "Chua Corsage Memristor Oscillator via Hopf Bifurcation." International Journal of Bifurcation and Chaos 26, no. 04 (April 2016): 1630009. http://dx.doi.org/10.1142/s0218127416300093.

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This paper demonstrates that the Chua Corsage Memristor, when connected in series with an inductor and a battery, oscillates about a locally-active operating point located on the memristor’s DC [Formula: see text]–[Formula: see text] curve. On the operating point, a small-signal equivalent circuit is derived via a Taylor series expansion. The small-signal admittance [Formula: see text] is derived from the small-signal equivalent circuit and the value of inductance is determined at a frequency where the real part of the admittance [Formula: see text] of the small-signal equivalent circuit of Chua Corsage Memristor is zero. Oscillation of the circuit is analyzed via an in-depth application of the theory of Local Activity, Edge of Chaos and the Hopf-bifurcation.

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Kavehei, O., A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi, and D. Abbott. "The fourth element: characteristics, modelling and electromagnetic theory of the memristor." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2120 (March 17, 2010): 2175–202. http://dx.doi.org/10.1098/rspa.2009.0553.

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In 2008, researchers at the Hewlett–Packard (HP) laboratories published a paper in Nature reporting the development of a new basic circuit element that completes the missing link between charge and flux linkage, which was postulated by Chua in 1971 (Chua 1971 IEEE Trans. Circuit Theory 18 , 507–519 ( doi:10.1109/TCT.1971.1083337 )). The HP memristor is based on a nanometre scale TiO 2 thin film, containing a— doped region and an undoped region. Further to proposed applications of memristors in artificial biological systems and non-volatile RAM, they also enable reconfigurable nanoelectronics. Moreover, memristors provide new paradigms in application-specific integrated circuits and field programmable gate arrays. A significant reduction in area with an unprecedented memory capacity and device density are the potential advantages of memristors for integrated circuits. This work reviews the memristor and provides mathematical and SPICE models for memristors. Insight into the memristor device is given via recalling the quasi-static expansion of Maxwell’s equations. We also review Chua’s arguments based on electromagnetic theory.

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GÜNAY, ENIS. "MLC CIRCUIT IN THE FRAME OF CNN." International Journal of Bifurcation and Chaos 20, no. 10 (October 2010): 3267–74. http://dx.doi.org/10.1142/s0218127410027659.

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A CNN-based nonautonomous chaotic oscillator circuit design is presented. Murali–Lakshmanan–Chua circuit, known as MLC circuit, is modeled by using CNN cells. The circuit implementation is supported by an eigenvalue study of the introduced system. The proposed model gives an alternative to MLC circuit with inductorless RC-based circuit realization.

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BARBOZA, RUY, and LEON O. CHUA. "THE FOUR-ELEMENT CHUA'S CIRCUIT." International Journal of Bifurcation and Chaos 18, no. 04 (April 2008): 943–55. http://dx.doi.org/10.1142/s0218127408020987.

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A new circuit configuration, linearly conjugate to the standard Chua's circuit, is presented. Its distinctive feature is that the equations now admit an additional parameter, which controls the dissipation in the network connected to the Chua diode. In the limiting case we obtain the simplest chaotic circuit, consisting of a piecewise-linear resistor and three lossless elements.

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To^rres, L. A. B., and L. A. Aguirre. "Extended chaos control method applied to Chua circuit." Electronics Letters 35, no. 10 (1999): 768. http://dx.doi.org/10.1049/el:19990560.

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Wang, Chunni, Zhilong Liu, Aatef Hobiny, Wenkang Xu, and Jun Ma. "Capturing and shunting energy in chaotic Chua circuit." Chaos, Solitons & Fractals 134 (May 2020): 109697. http://dx.doi.org/10.1016/j.chaos.2020.109697.

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ELHADJ, ZERAOULIA, and J. C. SPROTT. "GENERATING 3-SCROLL ATTRACTORS FROM ONE CHUA CIRCUIT." International Journal of Bifurcation and Chaos 20, no. 01 (January 2010): 135–44. http://dx.doi.org/10.1142/s0218127410025454.

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This paper reports the finding of a 3-scroll chaotic attractor with only three equilibria obtained via direct modification of Chua's circuit. In addition, it is shown numerically that the new system can also generate one-scroll and two-scroll chaotic attractors.

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BILOTTA, ELEONORA, and PIETRO PANTANO. "DISCRETE CHAOTIC DYNAMICS FROM CHUA'S OSCILLATOR: CHUA MACHINES." International Journal of Bifurcation and Chaos 19, no. 01 (January 2009): 1–115. http://dx.doi.org/10.1142/s0218127409022774.

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In previous work, the authors explored the parameter space for Chua's circuit and its generalizations, discovering new routes to chaos, and nearly a thousand new attractors. These were obtained by varying the parameters of the physical circuit and of systems derived from it. Here, we present a novel class of computational system that does not respect the classical constraints in Chua's circuit, and that generates chaotic dynamics via an iterative process based on discrete versions of the equations for Chua's circuit and its variants. We call these systems Chua Machines. After presenting the chaotic dynamics, we provide a formal description of Chua Machines and a Gallery of 222 3D images, illustrating their dynamics. We discuss the method used to discover these systems and the metrics applied in the exploration of their parameter space and offer examples of highly complex bifurcation maps, together with images showing how patterns can evolve with time, or vary significantly changing the values of one of the parameters. Finally, we present a detailed analysis of qualitative changes in a Chua Machine as it traverses the parameter space of the bifurcation map. The evidence suggests that these dynamics are even richer and more complex than their counterpart in the continuous domain.

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Murali, K., and M. Lakshmanan. "Synchronization through Compound Chaotic Signal in Chua's Circuit and Murali–Lakshmanan–Chua Circuit." International Journal of Bifurcation and Chaos 07, no. 02 (February 1997): 415–21. http://dx.doi.org/10.1142/s0218127497000285.

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In this letter the idea of synchronization of chaotic systems is further extended to the case where all the drive system variables are combined to obtain a compound chaotic drive signal. An appropriate feedback loop is constructed in the response system to achieve synchronization among the variables of drive and response systems. We apply this method of synchronization to the familiar Chua's circuit and Murali–Lakshmanan–Chua circuit equations.

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Cafagna, Donato, and Giuseppe Grassi. "Hyperchaotic Coupled Chua Circuits: An Approach for Generating New n×m-Scroll Attractors." International Journal of Bifurcation and Chaos 13, no. 09 (September 2003): 2537–50. http://dx.doi.org/10.1142/s0218127403008065.

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In this paper an approach for generating new hyperchaotic attractors from coupled Chua circuits is proposed. The technique, which exploits sine functions as nonlinearities, enables n×m-scroll attractors to be generated. In particular, it is shown that n×m-scroll dynamics can be easily designed by modifying four parameters related to the circuit nonlinearities. Simulation results are reported to illustrate the capability of the proposed approach.

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Yang Fang-Yan, Leng Jia-Li, and Li Qing-Du. "The 4-dimensional hyperchaotic memristive circuit based on Chua’s circuit." Acta Physica Sinica 63, no. 8 (2014): 080502. http://dx.doi.org/10.7498/aps.63.080502.

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Stankevich, Nataliya V., Nikolay V. Kuznetsov, Gennady A. Leonov, and Leon O. Chua. "Scenario of the Birth of Hidden Attractors in the Chua Circuit." International Journal of Bifurcation and Chaos 27, no. 12 (November 2017): 1730038. http://dx.doi.org/10.1142/s0218127417300385.

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Recently it was shown that in the dynamical model of Chua circuit both the classical self-excited and hidden chaotic attractors can be found. In this paper the dynamics of the Chua circuit is revisited. The scenario of the chaotic dynamics development and the birth of self-excited and hidden attractors is studied. A pitchfork bifurcation is shown in which a pair of symmetric attractors coexist and merge into one symmetric attractor through an attractor-merging bifurcation and a splitting of a single attractor into two attractors. The scenario relating the subcritical Hopf bifurcation near equilibrium points and the birth of hidden attractors is discussed.

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Yang, Chunde, Hao Cai, and Ping Zhou. "Stabilization of the Fractional-Order Chua Chaotic Circuit via the Caputo Derivative of a Single Input." Discrete Dynamics in Nature and Society 2016 (2016): 1–5. http://dx.doi.org/10.1155/2016/4129756.

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A modified fractional-order Chua chaotic circuit is proposed in this paper, and the chaotic attractor is obtained forq=0.98. Based on the Mittag-Leffler function in two parameters and Gronwall’s Lemma, two control schemes are proposed to stabilize the modified fractional-order Chua chaotic system via the Caputo derivative of a single input. The numerical simulation shows the validity and feasibility of the control scheme.

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CAFAGNA, DONATO, and GIUSEPPE GRASSI. "CHAOTIC BEATS IN A MODIFIED CHUA'S CIRCUIT: DYNAMIC BEHAVIOR AND CIRCUIT DESIGN." International Journal of Bifurcation and Chaos 14, no. 09 (September 2004): 3045–64. http://dx.doi.org/10.1142/s0218127404011181.

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This paper illustrates the recent phenomenon of chaotic beats in a modified version of Chua's circuit, driven by two sinusoidal inputs with slightly different frequencies. In order to satisfy the constraints imposed by the beats dynamics, a novel implementation of the voltage-controlled characteristic of the Chua diode is proposed. By using Pspice simulator, the behavior of the designed circuit is analyzed both in time-domain and state-space, confirming the chaotic nature of the phenomenon and the effectiveness of the approach.

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MURUGANANDAM, P., K. MURALI, and M. LAKSHMANAN. "SPATIOTEMPORAL DYNAMICS OF COUPLED ARRAY OF MURALI–LAKSHMANAN–CHUA CIRCUITS." International Journal of Bifurcation and Chaos 09, no. 05 (May 1999): 805–30. http://dx.doi.org/10.1142/s0218127499000572.

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The circuit recently proposed by Murali, Lakshmanan and Chua (MLC) is one of the simplest nonautonomous nonlinear electronic circuits which show a variety of dynamical phenomena including various bifurcations, chaos and so on. In this paper we study the spatiotemporal dynamics in one- and two-dimensional arrays of coupled MLC circuits both in the absence as well as in the presence of external periodic forces. In the absence of any external force, the propagation phenomena of traveling wavefront and its failure have been observed from numerical simulations. We have shown that the propagation of the traveling wavefront is due to the loss of stability of the steady states (stationary front) via subcritical bifurcation coupled with the presence of neccessary basin of attraction of the steady states. We also study the effect of weak coupling on the propagation phenomenon in one-dimensional array which results in the blocking of wavefront due to the existence of a stationary front. Further we have observed the spontaneous formation of hexagonal patterns (with penta–hepta defects) due to Turing instability in the two-dimensional array. We show that a transition from hexagonal to rhombic structures occur by the influence of an external periodic force. We also show the transition from hexagons to rolls and hexagons to breathing (space-time periodic oscillations) motion in the presence of external periodic force. We further analyze the spatiotemporal chaotic dynamics of the coupled MLC circuits (in one dimension) under the influence of external periodic forcing. Here we note that the dynamics is critically dependent on the system size. Above a threshold size, a suppression of spatiotemporal chaos occurs, leading to a space-time regular (periodic) pattern eventhough the single MLC circuit itself shows a chaotic behavior. Below this critical size, however, a synchronization of spatiotemporal chaos is observed.

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GLOVER, JAMES, and ALISTAIR MEES. "RECONSTRUCTING THE DYNAMICS OF CHUA'S CIRCUIT." Journal of Circuits, Systems and Computers 03, no. 01 (March 1993): 201–14. http://dx.doi.org/10.1142/s0218126693000150.

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The Chua circuit can be treated as a black box giving output which can be studied in a number of ways. This allows us to test some novel nonlinear system modeling methods. In particular, we show how to locate important dynamical features such as fixed points and near-heteroclinic cycles with very little effort, and then how to build a more detailed dynamical model to verify these discoveries.

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Saito, Yoshifuru, Iliana Marinova, and Hisashi Endo. "Parallel Ferroresonance Circuit Analysis by Chua-type Magnetization Model." IEEJ Transactions on Fundamentals and Materials 128, no. 8 (2008): 522–26. http://dx.doi.org/10.1541/ieejfms.128.522.

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Chakraborty, Satyabrata, and Syamal Kumar Dana. "Shil’nikov chaos and mixed-mode oscillation in Chua circuit." Chaos: An Interdisciplinary Journal of Nonlinear Science 20, no. 2 (June 2010): 023107. http://dx.doi.org/10.1063/1.3378112.

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Pourshaghaghi, Hamid Reza, Behnam Kia, William Ditto, and Mohammad Reza Jahed-Motlagh. "Reconfigurable logic blocks based on a chaotic Chua circuit." Chaos, Solitons & Fractals 41, no. 1 (July 2009): 233–44. http://dx.doi.org/10.1016/j.chaos.2007.11.030.

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Mira, Christian. "Chua's Circuit and the Qualitative Theory of Dynamical Systems." International Journal of Bifurcation and Chaos 07, no. 09 (September 1997): 1911–16. http://dx.doi.org/10.1142/s0218127497001497.

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Simple electronic oscillators were at the origin of many studies related to the qualitative theory of dynamical systems. Chua's circuit is now playing an equivalent role for the generation and understanding of complex dynamics. In honour of my friend Leon Chua on his 60th birthday.

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Zhang Xin-Guo, Sun Hong-Tao, Zhao Jin-Lan, Liu Ji-Zhao, Ma Yi-De, and Han Ting-Wu. "Equivalent circuit in function and topology to Chua’s circuit and the design methods of these circuits." Acta Physica Sinica 63, no. 20 (2014): 200503. http://dx.doi.org/10.7498/aps.63.200503.

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37

YANG, FANGYAN, QINGDU LI, and PING ZHOU. "HORSESHOE IN THE HYPERCHAOTIC MCK CIRCUIT." International Journal of Bifurcation and Chaos 17, no. 11 (November 2007): 4205–11. http://dx.doi.org/10.1142/s0218127407019743.

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The well-known Matsumoto–Chua–Kobayashi (MCK) circuit is of significance for studying hyperchaos, since it was the first experimental observation of hyperchaos from a real physical system. In this paper, we discuss the existence of hyperchaos in this circuit by virtue of topological horseshoe theory. The two disjoint compact subsets producing a horseshoe found in a specific 3D cross-section, both expand in two directions under the fourth Poincaré return map, this fact means that there exists hyperchaos in the circuit.

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38

ZHANG, YUANFAN, and XIANG ZHANG. "DYNAMICS OF THE MUTHUSWAMY–CHUA SYSTEM." International Journal of Bifurcation and Chaos 23, no. 08 (August 2013): 1350136. http://dx.doi.org/10.1142/s0218127413501368.

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The Muthuswamy–Chua system [Formula: see text] describes the simplest electronic circuit which can have chaotic phenomena. In this paper, we first prove the existence of three families of consecutive periodic orbits of the system when α = 0, two of which are located on consecutive invariant surfaces and form two invariant topological cylinders. Then we prove that for α > 0 if the system has a periodic orbit or a chaotic attractor, it must intersect both of the planes z = 0 and z = -1 infinitely many times as t tends to infinity. As a byproduct, we get an example of unstable invariant topological cylinders which are not normally hyperbolic and which are also destroyed under small perturbations.

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39

GUO, SHU-MEI, LEANG S. SHIEH, GUANRONG CHEN, and MARITZA ORTEGA. "ORDERING CHAOS IN CHUA'S CIRCUIT: A SAMPLED-DATA FEEDBACK AND DIGITAL REDESIGN APPROACH." International Journal of Bifurcation and Chaos 10, no. 09 (September 2000): 2221–31. http://dx.doi.org/10.1142/s0218127400001389.

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In this paper, we develop and apply some digital design and redesign techniques for ordering the chaotic Chua's circuit. The idea of using sampled-data feedback for controlling the circuit was previously suggested [Yang & Chua, 1998], which relies on small sampling periods. We show how this sampled-data feedback control method can be significantly improved, so that large sampling times are allowed, for the same purpose of ordering the nonlinear circuit, from anywhere within the chaotic attractor towards a predesired periodic cycle of the circuit.

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DANA, SYAMAL KUMAR, BRAJENDRA K. SINGH, SATYABRATA CHAKRABORTY, RAM CHANDRA YADAV, JÜRGEN KURTHS, GREGORY V. OSIPOV, PRODYOT KUMAR ROY, and CHIN-KUN HU. "MULTISCROLL IN COUPLED DOUBLE SCROLL TYPE OSCILLATORS." International Journal of Bifurcation and Chaos 18, no. 10 (October 2008): 2965–80. http://dx.doi.org/10.1142/s0218127408022196.

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A unidirectional coupling scheme is investigated in double scroll type chaotic oscillators that reveal interesting multiscroll dynamics. Instead of using self-oscillatory systems, in this scheme, double scroll chaos from one oscillator is forced into another similar oscillator in a resting state. This coupling scheme is explored in the Chua oscillator, a modified Chua oscillator and the Lorenz oscillator. We have modified the Chua oscillator by simply changing its piecewise linear function slightly, thereby deriving a new 3-scroll attractor. We have observed 4-scroll, 6-scroll attractors in the driven Chua oscillator and the modified Chua oscillator respectively in an intermittency regime of weaker coupling. We have extended the coupling scheme to the Lorenz system when even more interesting multiscroll dynamics (3-, 4-, 5-, 6-scroll) is observed with decreasing coupling strength. It appears as if a hidden multiscroll structure unfolds with weakening coupling interactions. One after another, additional scrolls appear in the driven Lorenz system when the coupling strength is gradually decreased in the weaker coupling regime. The origin of such multiscroll dynamics is explained using eigenvalue analysis and a bifurcation diagram. A schematic diagram of the multiscroll trajectories is presented to further elucidate the evolution of the scrolls. Experimental evidence is also presented using the Chua circuit and an electronic analog of the Lorenz system.

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41

OKSASOGLU, ALI, DONGSHENG MA, and QIUDONG WANG. "RANK ONE CHAOS IN SWITCH-CONTROLLED MURALI–LAKSHMANAN–CHUA CIRCUIT." International Journal of Bifurcation and Chaos 16, no. 11 (November 2006): 3207–34. http://dx.doi.org/10.1142/s0218127406016744.

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In this paper, we investigate the creation of strange attractors in a switch-controlled MLC (Murali–Lakshmanan–Chua) circuit. The design and use of this circuit is motivated by a recent mathematical theory of rank one attractors developed by Wang and Young. Strange attractors are created by periodically kicking a weakly stable limit cycle emerging from the center of a supercritical Hopf bifurcation, and are found in numerical simulations by following a recipe-like algorithm. Rigorous conditions for chaos are derived and various switch control schemes, such as synchronous, asynchronous, single-, and multi-pulse, are investigated in numerical simulations.

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Ma, Siyu, Ping Zhou, Jun Ma, and Chunni Wang. "Phase synchronization of memristive systems by using saturation gain method." International Journal of Modern Physics B 34, no. 09 (April 10, 2020): 2050074. http://dx.doi.org/10.1142/s0217979220500745.

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A variety of electric components can be used to bridge connection to the nonlinear circuits, and continuous pumping and consumption of energy are critical for voltage balance between the output end. The realization and stability of synchronization are mainly dependent on the physical properties of coupling channel, which can be built by using different electric components such as resistor, capacitor, induction coil and even memristor. In this paper, a memristive nonlinear circuit developed from Chua circuit is presented for investigation of synchronization, and capacitor, induction coil are jointed with resistor for building artificial synapse which connects one output of two identical memristive circuits. The capacitance and inductance of the coupling channel are carefully adjusted with slight step increase to estimate the threshold of coupling intensity supporting complete synchronization. As a result, the saturation gain method applied to realize the synchronization between chaotic circuits and physical mechanism is presented.

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Sundqvist, Kyle M., David K. Ferry, and Laszlo B. Kish. "Memristor Equations: Incomplete Physics and Undefined Passivity/Activity." Fluctuation and Noise Letters 16, no. 04 (November 21, 2017): 1771001. http://dx.doi.org/10.1142/s0219477517710018.

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In his seminal paper, Chua presented a fundamental physical claim by introducing the memristor, “The missing circuit element”. The memristor equations were originally supposed to represent a passive circuit element because, with active circuitry, arbitrary elements can be realized without limitations. Therefore, if the memristor equations do not guarantee that the circuit element can be realized by a passive system, the fundamental physics claims about the memristor as “missing circuit element” loses all its weight. The question of passivity/activity belongs to physics thus we incorporate thermodynamics into the study of this problem. We show that the memristor equations are physically incomplete regarding the problem of passivity/activity. As a consequence, the claim that the present memristor functions describe a passive device lead to unphysical results, such as violating the Second Law of thermodynamics, in infinitely large number of cases. The seminal memristor equations cannot introduce a new physical circuit element without making the model more physical such as providing the Fluctuation–Dissipation Theory of memristors.

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Aiping Jiang, Can He, and Xiangxue Zhang. "Image Watermarking Algorithm based on Contourlet and Chua��s Circuit." International Journal of Advancements in Computing Technology 4, no. 19 (October 31, 2012): 317–23. http://dx.doi.org/10.4156/ijact.vol4.issue19.38.

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Aiping Jiang, Bingliang Zhou, and Can He. "Image Encryption Algorithm Based on Contourlet and Chua��s circuit." International Journal of Digital Content Technology and its Applications 6, no. 15 (August 31, 2012): 120–28. http://dx.doi.org/10.4156/jdcta.vol6.issue15.15.

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Shi-Hong, Wang, Liu Wei-Qing, Ma Bao-Jun, Xiao Jing-Hua, and Jiang Da-Ya. "Phase synchronization of Chua circuit induced by the periodic signals." Chinese Physics 14, no. 1 (December 23, 2004): 55–60. http://dx.doi.org/10.1088/1009-1963/14/1/012.

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Chen, Mo, Jingjing Yu, and Bo‐Cheng Bao. "Finding hidden attractors in improved memristor‐based Chua''s circuit." Electronics Letters 51, no. 6 (March 2015): 462–64. http://dx.doi.org/10.1049/el.2014.4341.

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Korneta, W., E. Garcia-Moreno, and A. L. Sena. "Noise activated dc signal sensor based on chaotic Chua circuit." Communications in Nonlinear Science and Numerical Simulation 24, no. 1-3 (July 2015): 145–52. http://dx.doi.org/10.1016/j.cnsns.2014.12.010.

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BILOTTA, ELEONORA, GIANPIERO DI BLASI, FAUSTO STRANGES, and PIETRO PANTANO. "A GALLERY OF CHUA ATTRACTORS: PART IV." International Journal of Bifurcation and Chaos 17, no. 04 (April 2007): 1017–77. http://dx.doi.org/10.1142/s0218127407017665.

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The literature on Chua Oscillator includes more than a thousand papers, describing an astonishing variety of chaotic behavior. Gallery of Chua attractors, Part IV presents a collection of 101, previously unknown attractors, generated by a generalization of Chua circuit with a smooth nonlinear function. The gallery is the result of an extensive exploration of the parameter space for Chua cubic system, in which we used PCA and Hausdorf Distances to guide us. During this exploration we sensed the beauty of the chaotic patterns and recorded this beauty for the nonlinear community. The attractors we describe here represent only a small proportion of those we discovered during our exploration of phase space: much intensive research remains to be done. However, the very number of attractors we found suggests it might be possible not only to detect the morphogenetic processes which determine the points in phase space ("catastrophe points") where a family of attractors disappears and another one comes to life, but to identify more general "laws of morphogenesis" governing the behavior of these systems. In this paper, we outline five such rules.

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50

Hamdy, Mohamed, Mohamed Magdy, and Salah Helmy. "Control and synchronization for two Chua systems based on intuitionistic fuzzy control scheme: A comparative study." Transactions of the Institute of Measurement and Control 43, no. 7 (January 10, 2021): 1650–67. http://dx.doi.org/10.1177/0142331220981425.

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This paper presents control and synchronization for two nonlinear chaotic systems in the presence of uncertainties and external disturbances based on an intuitionistic fuzzy control (IFC) scheme. Two classes of Chua and cubic Chua oscillators have been formulated as master and slave respectively. The master and slave systems have different initial conditions and parameters, which leads to the butterfly effect that rules the chaotic systems’ behaviour. IFC scheme is chosen as a different method that has not been used before to control and synchronize Chua and cubic Chua oscillators. The main objective of the IFC scheme is to collect more information about the system and provide flexibility for the controller that increases the robustness of the control system to uncertainties in the structure of the chaotic systems. The stability analysis of the overall system is guaranteed using Routh-Hurwitz and Lyapunov criteria. The simulation results accomplished to evaluate the effectiveness of the proposed control and to demonstrate its reliability to control Chua’s circuit system with a comparative study.

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Journal articles on the topic 'Chua circuit'

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