Cited by 602Chaos control and synchronizationMathematical Dynamics and FractalsAdvanced Differential Equations and Dynamical Systems

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Chua's Circuit: A Paradigm for Chaos

Madan, Rabinder N·1993·World Scientific Series on Nonlinear Science Series B

DOI 10.1142/1997

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Abstract

For uninitiated researchers, engineers, and scientists interested in a quick entry into the subject of chaos, this book offers a timely collection of 55 carefully selected papers covering almost every aspect of this subject. Because Chua's circuit is endowed with virtually every bifurcation phenomena reported in the extensive literature on chaos, and because it is the only chaotic system which can be easily built by a novice, simulated in a personal computer, and tractable mathematically, it has become a paradigm for chaos, and a vehicle for illustrating this ubiquitous phenomenon. Its supreme

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Items 401–500 of 598

Dynamics of the forced negative conductance series LCR circuit
Pitchaimuthu, M. E., & Thamilmaran, K. (2020) · International Journal of Circuit Theory and Applications · doi:10.1002/cta.2729 · Cited by 5
“Equation (4) gives the normalized current g(x) flowing through the diode and negative impedance converter combination.”
Background
Existence of periodic solutions for differential equations with multiple delays under dichotomy condition
Ngiamsunthorn, P. S. (2015) · Advances in Difference Equations · doi:10.1186/s13662-015-0598-0 · Cited by 5
Controlling phase multistability in coupled period-doubling oscillators
Shabunin, A. V. (2013) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4772972 · Cited by 5
A CHEMICAL MODEL FOR CHUA'S EQUATION
Li, Q. S., & XU, W. (2002) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127402004760 · Cited by 5
“In comparison with the Lorenz model, Chua’s circuit is the simplest autonomous generator of chaotic signals [Chua, 1992] and is surely one of the most extensively studied chaotic circuits because of its simple circuit topology [Madan, 1993].”
BackgroundMethodInfluential
Wave propagation along interacting fiber-like lattices
Nekorkin, V. I., Kazantsev, V., Artyuhin, D. V., et al. (1999) · The European Physical Journal B · doi:10.1007/s100510051196 · Cited by 5
“by the following dimensionless coupled equations [13,14]  ẋ(1)j = α(y 1 j − x(1)j − f(x(1)j )) +D1∆x(1)j +hj(x(2)j − x(1)j ); ẏ(1) j = x 1 j − y(1) j + z(1) j ; ż(1) j = −βy1 j − γz(1) j ; ẋ(2)j = α(y 2 j − x(2)j − f(x(2)j )) +D2∆x(2)j +hj(x(1)j − x(2)j ); ẏ(2) j = x 2 j − y(2) j + z(2) j ; ż(2)…”
Influential
SET STABILIZATION OF A MODIFIED CHUA'S CIRCUIT
Li, S., & Tian, Y. (2005) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127405012181 · Cited by 5
“, 2002] which is a modified version of the famous Chua’s circuit [Madan, 1993].”
BackgroundMethod
BOIDS CONTROL OF CHAOS
Itoh, M., & Chua, L. O. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127407017525 · Cited by 5
A chaotic oscillator as a musical signal generator in an interactive performance system
Choi, I. (1997) · Journal of New Music Research · doi:10.1080/09298219708570715 · Cited by 5
OSCILLATIONS AND CHAOS IN SIMPLE QUADRATIC SYSTEMS
Innocenti, G., GENESIO, R., & GHILARDI, C. (2008) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127408021452 · Cited by 5
“This well-known electrical system (see e.g. [Madan, 1993]) can be described by the state equations ẋ1 = αx2 − mαx1 + αx31 ẋ2 = x1 − x2 + x3 ẋ3 = −βx2, (19) with a cubic function to represent smoothly the circuit nonlinearity.”
Nonlinear control of Chua's circuit
Márquez, R., & Sira-Ramirez, H. J. (2002) · doi:10.1109/mwscas.1995.504468 · Cited by 5
“‘Controlling chaos’ is actually an active area of research in which the physics, mathematics and the engineering communities have been very interested in the last few years ([l], [2], cf [3], [ 4 ] and references therein).”
Background
A NEW LOOK AT CHUA'S CIRCUIT
Gammoudi, I. E., & Feki, M. (2011) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127411029343 · Cited by 5
“Keywords : Chua circuit; LC oscillator; Wiene bridge oscillator; RC filter; RLC filter.”
Background
A chaos tracker applied to non-coherent detection in chaos-based digital communication systems
Feng, J., Tse, C. K., & Lau, F. C. M. (2002) · doi:10.1109/iscas.2001.921452 · Cited by 5
Self-organising behavior of arrays of nonidentical Josephson junctions
Fortuna, L., Frasca, M., & Rizzo, A. (2003) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.2002.1010678 · Cited by 5
Chaos in Nonlinear Electronic Circuits
Lakshmanan, M., & Rajasekar, S. (2003) · Advanced texts in physics · doi:10.1007/978-3-642-55688-3_6 · Cited by 5
LS-based Chaotic Oscillator
Zhou, C. (2002) · Physica Scripta · doi:10.1238/physica.regular.065a00025 · Cited by 5
Fractals in the twist-and-flip circuit
Chua, L. O., BROWN, R., & Hamilton, N. (1993) · Proceedings of the IEEE · doi:10.1109/5.241508 · Cited by 5
“For example, the simplest paradigm of "autonomous" chaos is given by Chua's circuit [1-3], which contains only one linear resis tor, one linear inductor, two linear capacitors, and a two-terminal nonlinear resistor called the Chua diode [4], Because of its mathematical tractability, more than 50 in-depth analyses ofCh…”
Background
Applications
Kapitaniak, T. (2000) · Springer eBooks · doi:10.1007/978-3-642-57143-5_6 · Cited by 4
Symmetry, chaos control and hysteresis in a second-order non-autonomous circuit with square-wave excitation
Srinivasan, K., Sivaganesh, G., Fozin, T. F., et al. (2024) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-024-05777-w · Cited by 4
“Most of the earlier works on the MLC circuit employ periodic excitation of the sinusoidal type only [12–14 , 31 ].”
Generation of Multiscroll Attractors by Controlling the Equilibria
Ontañon-García, L. J., Jiménez-López, E., & Campos-Cantón, E. (2012) · IFAC Proceedings Volumes · doi:10.3182/20120620-3-mx-3012.00024 · Cited by 4
Simple nonautonomous Wien-bridge oscillator based chaotic circuit
Rizwana, R., Mohamed, I. R., Srinivasan, K., et al. (2014) · International Conference on Devices, Circuits and Systems (ICDCS) · doi:10.1109/icdcsyst.2014.6926121 · Cited by 4
“devices or devices constructed with ingenious piecewise-linear elements have been utilized as veritable black boxes to explore different properties of chaotic dynamics [1-5].”
Background
A novel algorithm for efficient simulation of nonlinear transmission lines for RF applications via model order reduction
Nouri, B., Nakhla, M. S., & Achar, R. (2015) · IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization · doi:10.1109/nemo.2015.7415069 · Cited by 4
Memristors in Unconventional Computing: How a Biomimetic Circuit Element Can be Used to Do Bioinspired Computation
Gale, E. (2017) · Emergence, complexity and computation · doi:10.1007/978-3-319-33921-4_19 · Cited by 4
Cryptography with chaos using Chua's system
Oliveira, C. H., & Pizolato, J. C. (2011) · Journal of Physics Conference Series · doi:10.1088/1742-6596/285/1/012019 · Cited by 4
Fast Fourier Transform and Nonlinear Circuits Based Approach for Smart Meter Data Security
Babu, M. J., Sowmya, V., & Soman, K. P. (2015) · Procedia Technology · doi:10.1016/j.protcy.2015.10.031 · Cited by 4
FREQUENCY SWITCHED CHUA'S CIRCUIT: EXPERIMENTAL DYNAMICS CHARACTERIZATION
Cantelli, L., Fortuna, L., Frasca, M., et al. (2001) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127401002122 · Cited by 4
“The complete 2-D parameter bifurcation diagram of the Chua’s circuit is reported in [Madan, 1993], along with several examples of the strange attractors which can be obtained.”
Influential
On the Mechanisms Behind Chaos
Lindberg, E. (2006) · Nonlinear Dynamics · doi:10.1007/s11071-006-1972-y · Cited by 4
A MODIFIED CHUA CIRCUIT SIMULATES 1/f-LIKE FLUCTUATION OF HEARTBEAT INTERVALS
Osaka, M., & Watanabe, M. (2004) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127404011429 · Cited by 4
NEW CONSTRUCTION OF MIXED-MODE CHAOTIC CIRCUITS
Klomkarn, K., Sooraksa, P., & Chen, G. (2010) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127410026630 · Cited by 4
“In the past two decades, after the invention of Chua’s circuit [Madan, 1993], several designs of chaotic oscillators have been developed.”
Background
Estimation of Magnitude of Self-Induced Oscillations via Piecewise Quadratic Lyapunov Functions
Hu, T., & Jung, H. (2011) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2011.2157747 · Cited by 4
“In many chaotic systems, the oscillation occurs within a global attractor (e.g., see [5], [11], [19], [22], [23], [ 27 ], [28], [29], [35], [43], [45]).”
Background
Coexistence of excitability, Hopf and Turing modes in a one-dimensional array of nonlinear circuits
Gómez-Gesteira, M., Pérez-Muñuzuri, V., Chua, L. O., et al. (1995) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.473573 · Cited by 4
STABILIZATION OF GLOBAL INVARIANT SETS FOR CHAOTIC SYSTEMS: AN ENERGY BASED CONTROL APPROACH
Laval, L., & M’Sirdi, N. K. (2002) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127402005182 · Cited by 4
“For this purpose, we consider the chaotic circuit of Chua (e.g. [Madan, 1993; Yang & Chua, 1998]) depicted in Fig.”
Method
The d/sub /spl infin// parameter to characterise chaotic dynamics
Bonasera, A., Bucolo, M., Fortuna, L., et al. (2000) · doi:10.1109/ijcnn.2000.861529 · Cited by 4
Generation of Multistability through Unstable Systems
Díaz-González, E.-C., GUERRA-LÓPEZ, A., Aguirre‐Hernández, B., et al. (2022) · Chaos Theory and Applications · doi:10.51537/chaos.1196860 · Cited by 3
Performance enhancement energy harvesting from aeroelastic vibrations using a van der Pol circuit
Moussati, Y. E., & Hamdi, M. (2024) · Mechanics Based Design of Structures and Machines · doi:10.1080/15397734.2024.2411267 · Cited by 3
“Finally, we note that the van der Pol circuit, utilized in this work, can be realized by two elements: an inductor and a memristor or by three elements: an inductor, a capacitor, and a volt-age-controlled memristor (Dumitrescu et al. 2012; Itoh and Chua 2014; Lu et al. 2014; Madan 1993).”
Observation of spontaneous bursting spike patterns in simple three memristor circuits
Gale, E., Costello, B. D. L., & Adamatzky, A. (2013) · European Conference on Circuit Theory and Design · doi:10.1109/ecctd.2013.6662330 · Cited by 3
“Chua’s circuit is the simplest built electronic circuit that can exhibit chaotic behaviour [12].”
Background
Periodic orbits in hysteretic systems with real eigenvalues
Esteban, M., Ponce, E., & Torres, F. (2019) · Nonlinear Dynamics · doi:10.1007/s11071-019-05148-6 · Cited by 3
Heteroclinic Cycles Generated by Piecewise Affine Systems in ℝn
Lu, K., Xu, W., Wei, Y., et al. (2022) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127422501462 · Cited by 3
Synchronisation behaviour between two candle flame oscillators with similar and dissimilar amplitudes of oscillations
Bhattacharya, A., Mondal, S., De, S., et al. (2023) · Combustion Theory and Modelling · doi:10.1080/13647830.2023.2165966 · Cited by 3
CMOS cryptosystem using a Lorenz chaotic oscillator
Gonzalez, O. A., Han, G., de Gyvez, J. P., et al. (2003) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.1999.777604 · Cited by 3
Electronic Circuit Simulation of the Lorenz Model With General Circulation
Saha, D. C., Ray, A., & Chowdhury, A. R. (2014) · International Journal of Physics · doi:10.12691/ijp-2-5-1 · Cited by 3
“This approach got a boosting with the advent of Chua’s circuit [2,3,4].”
Method
Numerical Bifurcation Analysis of Electronic Circuits
Freire, E., & Rodríguez-Luis, A. J. (2007) · Understanding complex systems · doi:10.1007/978-1-4020-6356-5_7 · Cited by 3
Modeling, Fabrication, and Characterization of Memristors
Mazady, A. (2014) · Cited by 3
A MODIFIED CHUA CIRCUIT SIMULATES A V-SHAPED TROUGH IN AUTONOMIC ACTIVITY AS A PRECURSOR OF SUDDEN CARDIAC DEATH
Osaka, M. (2011) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127411030040 · Cited by 3
“, 1988], (2) the modified Chua circuit for HR, SNA, and BP can simulate the steeper slope when the interaction between SNA and BP is reduced, (3) such a reduced interaction is considered to cause the steeper scaling slope of HR in the patients with postmyocardial infarction [Bigger et al., 1996], who have the poor pro…”
Influential
Theory of Fuzzy Chaos for the Simulation and Control of Nonlinear Dynamical Systems
Castillo, O., & Melín, P. (2006) · Springer eBooks · doi:10.1007/3-540-32502-6_14 · Cited by 3
CONTROLLED PARAMETER MODULATIONS IN SECURE DIGITAL SIGNAL TRANSMISSIONS
Palaniyandi, P., & Lakshmanan, M. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s021812740701972x · Cited by 3
A new butterfly attractor based on Chua's circuit and its application in security communication
Li, J., Lu, M., Zhang, W., & Qian, Y. (2013) · IEEE Region 10 Conference (TENCON) · doi:10.1109/tencon.2013.6718485 · Cited by 3
“As Chua’s circuit is easy to be constructed, it is considered as the paradigm for chaos and the real life existing proof of chaos [5], [6].”
Background
Synchronization analysis of networks of identical and nearly identical Chua's oscillators
Mishkovski, I., Mirchev, M., Corinto, F., et al. (2012) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.2012.6271703 · Cited by 3
Evaluation of a chaotic switching scheme for power converters
Tse, K. K., Ng, W. M., Chung, H. S.-H., et al. (2002) · PESC record · doi:10.1109/pesc.2000.878891 · Cited by 3
On the complexity of periodic and nonperiodic behaviors of a hysteresis-based electronic oscillator
Stellardo, D., Bizzarri, F., Storace, M., et al. (2007) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2778552 · Cited by 3
Robust fault-sensitive synchronization of a class of nonlinear systems
Xu, S., Yang, Y. Z., Liu, X., et al. (2011) · Chinese Physics B · doi:10.1088/1674-1056/20/2/020509 · Cited by 3
Generation of Hyperchaotic Chua System via State Feedback Control
Xi, H., Yu, S., Zhang, Z., et al. (2010) · doi:10.1109/iwcfta.2010.45 · Cited by 3
“Chua system is one of the best known and studied physical systems displaying chaotic behavior [1]–[3].”
Background
Detecting interactions in discrete-time dynamics by random variable resetting
Deng, C., Jiang, W., & Wang, S. (2021) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0028411 · Cited by 3
Mesoscopic description of a chemical bistable state
Zhu, R., & Li, Q. S. (2002) · The Journal of Chemical Physics · doi:10.1063/1.1446843 · Cited by 3
ON STABILIZING N-DIMENSIONAL CHAOTIC SYSTEMS
Laval, L., & M’Sirdi, N. K. (2003) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127403006650 · Cited by 3
“For this purpose, we consider the chaotic circuit of Chua as defined in [Madan, 1993; Yang & Chua, 1998].”
Method
Self-organisation in arrays of nonlinear systems induced by chaotic perturbation: An experimental approach
Arena, P., Fortuna, L., Porto, D., et al. (2003) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.1999.777613 · Cited by 3
Nonlinearities: Your worst enemies…? … Your best friends!
OGORZAŁEK, M. J. (2007) · European Conference on Circuit Theory and Design · doi:10.1109/ecctd.2007.4529701 · Cited by 3
“One of the simplest circuits generating chaotic solutions is Chua’s circuit [11] consisting of two linear capacitors, linear inductor and one linear and one nonlinear resistor.”
Background
The Importance of Strange Attractors for Industrial Mathematics
Lozi, R. (2002) · Applied optimization · doi:10.1007/978-1-4613-0263-6_12 · Cited by 3
STATISTICAL ESTIMATION OF THE EMBEDDING DIMENSION OF A DYNAMICAL SYSTEM
Bosq, D., Guégan, D., & Léorat, G. (1999) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127499000456 · Cited by 3
Chaos generators based on yttrium-iron garnet films for communication systems with a chaotic synchronous response
Mezin, N. I., Glushchenko, A. A., & Kuzovlev, Y. E. (2012) · Technical Physics Letters · doi:10.1134/s1063785012100082 · Cited by 2
On the existence of chaos in the Chua's circuit with a smooth nonlinearity
Galias, Z. (2016) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.2016.7527438 · Cited by 2
“The problem of existence of chaos in this system has been studied extensively since the invention of the circuit [1], [2].”
Background
A direct transition to chaos in hysteretic systems with focus dynamics
Esteban, M., Ponce, E., & Torres, F. (2019) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.5115101 · Cited by 2
Synchronization Analysis of Neuronal Networks by Means of Recurrence Plots
Bergner, A., Romano, M. C., Kurths, J., et al. (2007) · Springer eBooks · doi:10.1007/978-3-540-73159-7_6 · Cited by 2
Three-Dimensional Autonomous Systems and Chaos
Lynch, S. (2014) · Springer eBooks · doi:10.1007/978-3-319-06820-6_14 · Cited by 2
ON NONLINEAR CIRCUIT COMPONENTS WITH N-SHAPED CONDUCTANCE CHARACTERISTICS
Wey, T. A., & Ogborn, L. L. (1995) · Purdue e-Pubs (Purdue University System) · Cited by 2
Rapid prototyping of chaotic generators using LabView-FPGA
Castro, H., & Taborda, J. A. (2012) · doi:10.1109/cwcas.2012.6404075 · Cited by 2
“Many references can be found about bifurcation scenarios with chaos attractors, either in theoretical research [3], [4] or in practical research [5], [6].”
Background
Reduced‐order impulsive control for a class of nonlinear systems
Wang, Y., Wen, C., Soh, Y. C., et al. (2009) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.1478 · Cited by 2
RESIDENCE TIME DISTRIBUTIONS FOR DOUBLE-SCROLL ATTRACTORS
Grete, P., & Markus, M. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127407017720 · Cited by 2
Structure identification based on steady-state control: Experimental results and applications
Frasca, M., Yu, D., & Fortuna, L. (2010) · Physical Review E · doi:10.1103/physreve.81.026212 · Cited by 2
DID ARTISTS DISCOVER CHAOS BEFORE SCIENTISTS?
Fortuna, L., & Frasca, M. (2010) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127410026253 · Cited by 2
“In 1983, twenty years after the Lorenz’s discovery, the first electronic circuit able to show an intentionally designed chaotic behavior was invented by Leon Chua [Madan, 1993; Fortuna et al., 2009].”
Background
STOCHASTIC SIMULATION OF CHEMICAL CHUA SYSTEM
Li, Q. S., & Zhu, R. (2004) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127404009582 · Cited by 2
Construction of Central Pattern Generator Using Piecewise Affine Systems
Lee, W. M., & Yam, Y. (2007) · International Conference on Control and Automation · doi:10.1109/icca.2007.4376657 · Cited by 2
“For example, Chua [14] created a framework of chaotic systems from piecewise affine systems.”
Background
CHARACTERIZATION OF CHAOS SCENARIOS WITH PERIODIC INCLUSIONS FOR ONE CLASS OF PIECEWISE-SMOOTH DYNAMICAL MAPS
Taborda, J. A., Angulo, F., & Olivar, G. (2011) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127411029975 · Cited by 2
RANK ONE CHAOS IN SWITCH-CONTROLLED PIECEWISE LINEAR CHUA'S CIRCUIT
Wang, Q., & Oksasoglu, A. (2007) · Journal of Circuits Systems and Computers · doi:10.1142/s0218126607003976 · Cited by 2
A noise reduction method for noisycontaminated chaotic signal
Feng, J., & Xie, S. (2005) · International Conference on Communications, Circuits and Systems · doi:10.1109/icccas.2005.1495317 · Cited by 2
Connections of Multi Memristors
Sun, J., Wang, Y., & Cui, G. (2015) · Communications in computer and information science · doi:10.1007/978-3-662-49014-3_35 · Cited by 2
A didactic electronic set-up for introducing to complex networks of chaotic oscillators
de Magistris, M., Yaghouti, S., Corti, L., et al. (2016) · IEEE Global Engineering Education Conference (EDUCON) · doi:10.1109/educon.2016.7474647 · Cited by 2
Sudden Cardiac Death from the Perspective of Nonlinear Dynamics
Osaka, M. (2018) · Journal of Nippon Medical School · doi:10.1272/jnms.2018_85-2 · Cited by 2
A Unified Approach to Piecewise Linear Hopf and Hopf-Pitchfork Bifurcations
Ponce, E., Ros, J., & Vela, E. (2015) · Springer proceedings in mathematics & statistics · doi:10.1007/978-3-319-12583-1_12 · Cited by 2
“More recently, the analysis of piecewise linear systems received growing attention due to the interest on PWL chaotic systems, see for instance [10] and references therein.”
Background
Sound Synthesis and Chaotic Behaviour in Chua's Oscillator
Bilotta, E., Campolo, R., Pantano, P., et al. (2006) · Mathematics in industry · doi:10.1007/978-3-540-32862-9_41 · Cited by 2
Recent advances in the transmission of information using a chaotic signal
Hasler, M. (1997) · Cited by 2
Single Memristor Logic Gates: From NOT to a Full AdderPreprint
Gale, E. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1510.05705 · Cited by 2
“Brain dynamics are known to be chaotic and it has been suggested that neurons are poised at the edge of chaos [20], so the search for chaos using memristors (a search also inspired by the similarity of the memristor’s operation to the Chua diode in Chua’s circuit [24, 25] – the simplest chaotic circuit) is”
Method
POINCARÉ PLANES IN NONLINEAR ELECTRONICS
Campos-Cantón, E., GONZÁLEZ, J. S., & Urı́as, J. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127407017264 · Cited by 2
“2 2For an overview see [Rulkov, 1996] and [Madan, 1993]. where a hypothetical orbit is shown, projected onto the x1–x2 plane, and the edges of the squared waveform s(t) coincide with the times the orbit crosses the plane, which is projected as the line x2 = mx1 + (q2 −mq1) in Fig.”
BackgroundMethod
Mechanism for antiphase synchronization in neuron models
Postnov, D. E., & Han, S. K. (1999) · Technical Physics Letters · doi:10.1134/1.1262406 · Cited by 2
CHUA'S PERIODIC TABLE
Tonelli, R., & Meloni, F. (2002) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127402005406 · Cited by 2
“Among all nonlinear systems Chua's circuit [Madan, 1993] plays a special role in view of its simplicity and rich dynamics, including the possibility to exhibit an immense variety of chaotic attractors.”
Influential
Evolution of chaos in the Matsumoto-Chua circuit: a symbolic dynamics approach
Maranhão, D. M., & Prado, C. P. C. (2005) · Brazilian Journal of Physics · doi:10.1590/s0103-97332005000100013 · Cited by 2
“been explored extensively in previous works (see for example [8]).”
Background
Differential Equations for the Components of the Canonical Chua's Circuit and its General Properties
Samoilenko, A. M., & Chua, L. O. (1994) · Journal of Nonlinear Mathematical Physics · doi:10.2991/jnmp.1994.1.1.2 · Cited by 2
Control of chaotic systems with improved performance using modified backstepping and genetic algorithms
Grinits, E. V., & Bottura, C. P. (2003) · IEEE International Symposium on Intelligent Control · doi:10.1109/isic.2003.1254673 · Cited by 2
Jump resonance in the driven Chua's circuit to design frequency selective devices
Buscarino, A., Famoso, C., & Fortuna, L. (2024) · International Journal of Circuit Theory and Applications · doi:10.1002/cta.4237 · Cited by 1
Design and Evaluation of Chaos-Based Excitation Strategies for Brushless DC Motor Drives: A Multi-Domain Framework for Application-Specific Selection
Shafique, A., Kolev, G. Y., Bayazitov, O., et al. (2026) · Designs · doi:10.3390/designs10020033 · Cited by 1
“…subsequent normalized state-space representation have been widely studied since Chua’s original work [8] and comprehensively analyzed by Kennedy [9] and Madan [10] for circuit implementation and parameter selection, with the 1993 monograph [13] providing a comprehensive explanation of the paradigm.”
Influential
Quasi-periodic structures and “shrimps” in chaos on the example of a two-mode van der Pol generator
Кузнецов, А. П., Sataev, I. R., & Stankevich, N. V. (2026) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0334000 · Cited by 1
Mapping atoms to nonlinear Chua's circuits
Tonelli, R., Chua, L. O., & Meloni, F. (2003) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.2002.1010162 · Cited by 1
Selected general problems in chaos theory and nonlinear dynamics
Petržela, J., & Götthans, T. (2011) · International Conference on Mathematical Methods and Computational Techniques in Electrical Engineering · Cited by 1
Another Chemical Chaotic Attractor for Chua's Equation
Xu, W. G., & Li, Q. S. (2003) · International Journal of Bifurcation and Chaos · doi:10.1142/s021812740300820x · Cited by 1
A novel algorithm for optimum order estimation of nonlinear reduced macromodels
Nouri, B., Nakhla, M. S., & Achar, R. (2013) · IEEE Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS) · doi:10.1109/epeps.2013.6703484 · Cited by 1
THE FRACTIONAL ORDER MODIFIED CHAOTIC n-SCROLL CHUA CIRCUIT AND FRACTIONAL CONTROL
Sun, G., & Wang, M. (2012) · International Journal of Modern Physics B · doi:10.1142/s0217979212500750 · Cited by 1
PERIOD-DOUBLING AND SCROLL-DOUBLING BIFURCATIONS IN A CLASS OF NONSYMMETRIC CELLULAR NEURAL NETWORKS
Tang, C., ZENG, K., & Chen, F. (2008) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127408022469 · Cited by 1
Novel method of chaotic systems evaluation for implementations of encryption algorithms
Dutra, É., Glesner, M., Finamore, W. A., & Indrusiak, L. S. (2010) · doi:10.1109/ictel.2010.5478834 · Cited by 1
“Since then, more than twenty non-linear differential equations systems with chaotic behavior have being reported [1, 2 , 3, 4, 5, 6, 15].”
Background
Use of Chaos to Improve Equipments
Fortuna, L., & Frasca, M. (2007) · Springer eBooks · doi:10.1007/3-540-33878-0_1 · Cited by 1
Purely Imaginary Eigenvalues (PIE) in Extended Circuits with Mem-Devices
Oke, A. A. (2014) · IOSR Journal of Electrical and Electronics Engineering · doi:10.9790/1676-09340108 · Cited by 1
“Nonetheless, these latter memory systems are still of great importance since they provide a complex functionality within a single electronic structure.”
Background
Three-Dimensional Autonomous Systems and Chaos
Lynch, S. (2004) · Birkhäuser Boston eBooks · doi:10.1007/978-0-8176-8156-2_14 · Cited by 1

Authors: Madan, R. N.
Affiliations: Office of Naval Research (US)
Corresponding author: Madan, Rabinder N
Venue: World Scientific Series on Nonlinear Science Series B
Publisher: WORLD SCIENTIFIC
Published: 1993-11
ISSN: 1793-1029 (ISSN-L)
DOI: 10.1142/1997
OpenAlex: W1599681710
Cited by: 602
References: 0
Citations by year: 2026: 7 · 2025: 3 · 2024: 7 · 2023: 4 · 2022: 7 · 2021: 4 · 2020: 11 · 2019: 14 · 2018: 13 · 2017: 12 · 2016: 13 · 2015: 15 · 2014: 19 · 2013: 16 · 2012: 19
FWCI: 6.41
Type: book
Language: en
Open access: closed
Locations: World scientific series on nonlinear science, series B (publishedVersion)
CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
Topics: Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Equations and Dynamical Systems
Keywords: Chua's circuit, chaos, nonlinear dynamics, bifurcation, chaotic systems, circuit simulation

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Chua's Circuit: A Paradigm for Chaos

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