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 201–300 of 598

Chaos and structures in a chain of mutually-coupled Chua's circuits
Osipov, G. V., & Shalfeev, V. D. (1995) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.473576 · Cited by 22
“Chua’s circuit is known to be a selfoscillatory cell with complex dynamics the inherent features of which are the existence of two stable equilibrium states and periodic oscillations of different types, including chaotic oscillations [ 4 ], [5].”
Background
Two Twin-T based op amp oscillators modified for chaos
Elwakil, A. S., & Soliman, A. M. (1998) · Journal of the Franklin Institute · doi:10.1016/s0016-0032(97)00008-2 · Cited by 22
Motion around a monopole + ring system - I. Stability of equatorial circular orbits versus regularity of three-dimensional motion
Ramos-Caro, J., Pedraza, J. F., & Letelier, P. S. (2011) · Monthly Notices of the Royal Astronomical Society · doi:10.1111/j.1365-2966.2011.18618.x · Cited by 20
“It is the first example where the existence of such class of function leads to the existence of a chaotic attractor in a dynamical system (Madan 1993).”
Background
A bifurcation analysis of a simple electronic circuit
Algaba, A., Gamero, E., & Rodríguez-Luis, A. J. (2003) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/s1007-5704(03)00104-7 · Cited by 21
OBSERVER-BASED ADAPTIVE FEEDBACK CONTROLLER OF A CLASS OF CHAOTIC SYSTEMS
Boulkroune, A., Chekireb, H., Tadjine, M., et al. (2006) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127406016896 · Cited by 21
Further investigation on trajectory of chaotic guiding signals for robotic systems
Klomkarn, A. J. K., & Sooraksa, P. (2005) · IEEE International Symposium on Communications and Information Technology (ISCIT) · doi:10.1109/iscit.2004.1413902 · Cited by 21
Noise-enhanced temporal regularity in coupled chaotic oscillators
Lai, Y., & Liu, Z. (2001) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.64.066202 · Cited by 21
A universal circuit for studying chaotic phenomena
Chua, L. O., Pivka, L., & Wu, C. W. (1995) · Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences · doi:10.1098/rsta.1995.0091 · Cited by 21
Nonlinear waves, patterns and spatio-temporal chaos in cellular neural networks
Pérez-Muñuzuri, V., Muñuzuri, A. P., Gómez-Gesteira, M., et al. (1995) · Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences · doi:10.1098/rsta.1995.0093 · Cited by 21
The K.U.Leuven Time Series Prediction Competition
Suykens, J. A. K., & Vandewalle, J. P. L. (1998) · Springer eBooks · doi:10.1007/978-1-4615-5703-6_9 · Cited by 21
“For the parameters α = 9, β = 14.286 and the vectors m = [m0m1 · · ·m2q−1], c = [c1 c2 · · · c2q−1] one obtains • q = 1: double scroll (2-scroll) [Chua et al., 1986; Chua, 1994; Madan, 1993] m = [−1/7 + 2/7] c = 1 (3) • q = 3: 5-scroll [Suykens et al., 1997] m = [0.9/7 − 3/7 3.5/7 − 2.7/7 4/7 −…”
Influential
Control and applications of chaos
Grebogi, C., Lai, Y.-C., & Hayes, S. T. (1997) · Journal of the Franklin Institute · doi:10.1016/s0016-0032(97)00040-9 · Cited by 21
On comparison of attractors for chaotic mobile robots
Jansri, A., Klonikarn, K., & Sooraksa, P. (2005) · doi:10.1109/iecon.2004.1432201 · Cited by 20
Synchronization-based computation through networks of coupled oscillators
Malagarriga, D., García-Vellisca, M. A., Villa, A. E. P., Buldú, J. M., García‐Ojalvo, J., & Pons, A. J. (2015) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2015.00097 · Cited by 22
Turnpike Theorem for an Infinite Horizon Optimal Control Problem with Time Delay
Mammadov, M. A. (2014) · SIAM Journal on Control and Optimization · doi:10.1137/130926808 · Cited by 20
“Some other applications are in epidemiology and population dynamics [13, 23], laser optics [29, 33], power systems and neural networks [2, 13, 25, 49], physiological processes [16, 3, 33], life sciences and economics [12, 27], and other natural sciences [12, 29].”
Background
An experimental study on SC-CNN based canonical Chua’s circuit
Swathy, P. S., & Thamilmaran, K. (2012) · Nonlinear Dynamics · doi:10.1007/s11071-012-0677-7 · Cited by 20
EVOLUTIONARY DYNAMICS CAN BE CHAOTIC: A FIRST EXAMPLE
Dercole, F., & Rinaldi, S. (2010) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127410027829 · Cited by 20
“…fields of science, starting with meteorology [Lorenz, 1963], where the first strange attractor has been found, and proceeding with mechanics [Hayashi et al., 1970], chemistry [Rössler, 1976], electronics [Madan, 1993], epidemiology [Schwartz & Smith, 1983], and ecology [Hastings & Powell, 1991].”
Background
AN ANALYTICAL PREDICTION OF PERIODIC FLOWS IN THE CHUA CIRCUIT SYSTEM
Luo, A. C. J., & XUE, B. (2009) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127409023998 · Cited by 20
Transmission characteristics study of memristors based Op-Amp circuits
Qin, Y., Qin, Z., Yu, J., & Mao, Y. (2009) · International Conference on Communications, Circuits and Systems · doi:10.1109/icccas.2009.5250356 · Cited by 20
Experimental observation of generalized time-lagged chaotic synchronization
Zhu, L., & Lai, Y. (2001) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.64.045205 · Cited by 20
Applications of some mathematical methods in the analysis of cellular neural networks
Slavova, A. (2000) · Journal of Computational and Applied Mathematics · doi:10.1016/s0377-0427(99)00277-0 · Cited by 20
Additive nonparametric reconstruction of dynamical systems from time series
Abel, M., Ahnert, K., Kurths, J., et al. (2005) · Physical Review E · doi:10.1103/physreve.71.015203 · Cited by 20
“In the following, the procedure is illustrated by the example of a modified Chua circuit [9] with a third order nonlinearity.”
Method
Is the Colpitts oscillator a relative of Chua's circuit?
Sarafian, G., & Kaplan, B. Z. (1995) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.390275 · Cited by 20
Experimental characterization of nonlinear systems: a real-time evaluation of the analogous Chua’s circuit behavior
Rocha, R., Andrucioli, G. L. D., & Medrano-T, R. O. (2010) · Nonlinear Dynamics · doi:10.1007/s11071-010-9714-6 · Cited by 19
“Since its initial proposal, the Chua’s circuit is intensely investigated and has been accepted as paradigm for study of important features of nonlinear systems, once it exhibits a very complex dynamical behavior in spite of its simplicity [4].”
Background
Hyperchaos and bifurcations in a driven Van der Pol–Duffing oscillator circuit
Vincent, U. E., Nbendjo, B. R. N., Ajayi, A. A., et al. (2014) · International Journal of Dynamics and Control · doi:10.1007/s40435-014-0118-1 · Cited by 19
Stability Analysis and Mapping of Multiple Dynamics of Chua’s Circuit in Full Four-Parameter Spaces
Rocha, R., & Medrano-T, R. O. (2015) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127415300372 · Cited by 19
“…allows to observe a large and diverse set of dynamic behaviors, such as equilibrium points, periodic and stranger attractors, period doubling, Andronov–Hopf and homoclinic bifurcations, and hidden oscillations [Madan, 1993; Medrano-T. et al., 2005; Algaba et al., 2012; Leonov & Kuznetsov, 2013].”
Background
Anticipating, complete and lag synchronizations in RC phase-shift network based coupled Chua’s circuits without delay
Srinivasan, K., Senthilkumar, D. V., Mohamed, I. R., et al. (2012) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4711375 · Cited by 19
“The standard Chua’s circuit [4, 26] contains an LC oscillator connected to a nonlinear element, namely a Chua’s diode through an RC circuit.”
Method
Combined Chaotic Attractor Mobile Robots
Chanvech, C., Klomkarn, K., & Sooraksa, P. (2006) · SICE-ICASE International Joint Conference · doi:10.1109/sice.2006.314716 · Cited by 19
Numerical and experimental investigation of the effect of filtering on chaotic symbolic dynamics
Zhu, L., Lai, Y., Hoppensteadt, F. C., et al. (2003) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.1520090 · Cited by 19
How state controlled CNN cells generate the dynamics of the Colpitts-like oscillator
Arena, P., Baglio, S., Fortuna, L., et al. (1996) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.508183 · Cited by 19
Design of noncoherent receiver for analog spread-spectrum communication based on chaotic masking
Murali, K., Leung, H., & Yu, H. (2003) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/tcsi.2003.808905 · Cited by 19
Investigation of chaos in large arrays of Chua's circuits via a spectral technique
Gilli, M. (1995) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.473589 · Cited by 19
“In the electrical engineering community, many researchers concentrated on the study of large arrays made of Chua’s circuits (that is, a simple and robust example of chaotic oscillator [5], [ 6 ]); it has been shown that such arrays may model the propagation failure phenomenon [8] and may have application in image proc…”
Background
On Bifurcations Leading to Chaos in Chua's Circuit
Bykov, V. V. (1998) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127498000486 · Cited by 18
Dichotomy of nonlinear systems: Application to chaos control of nonlinear electronic circuit
Wang, J., Duan, Z., & Huang, L. (2005) · Physics Letters A · doi:10.1016/j.physleta.2005.10.072 · Cited by 18
TIME-DELAYED IMPULSIVE CONTROL OF CHAOTIC HYBRID SYSTEMS
Tian, Y., Yu, X., & Chua, L. O. (2004) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127404009612 · Cited by 18
Chaotic synchronization in small assemblies of driven Chua's circuits
Sanchez, E., Matı́as, M. A., & Pérez-Muñuzuri, V. (2000) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.847871 · Cited by 18
“, [39]) can be characterized by the following set of differential equations:”
Background
Complex dynamical behaviours in two non-linearly coupled Chua’s circuits
Cincotti, S., & Stefano, S. D. (2004) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2003.12.029 · Cited by 19
Fault-tolerant synchronization for nonlinear switching systems with time-varying delay
Liu, X., & Wu, C. (2016) · Nonlinear Analysis Hybrid Systems · doi:10.1016/j.nahs.2016.06.005 · Cited by 17
Generalized multistable structure via chaotic synchronization and preservation of scrolls
Jiménez-López, E., Salas, J. S. G., Ontañon-García, L. J., et al. (2013) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2013.06.025 · Cited by 17
“Other approaches imply the modification of the Chua's system [20,21] by replacing the nonlinear term with different nonlinear functions [22,23].”
Method
Adaptive event-triggered prescribed performance learning synchronization for complex dynamical networks with unknown time-varying coupling strength
Fan, A., Li, J., & Li, J. (2020) · Nonlinear Dynamics · doi:10.1007/s11071-020-05648-w · Cited by 17
Coherence resonance in chaotic electronic circuits
Calvo, O., Mirasso, C. R., & Toral, R. (2001) · Electronics Letters · doi:10.1049/el:20010735 · Cited by 17
A Chaotic Circuit with Ferroelectric Nonlinearity
Fortuna, L., Frasca, M., Graziani, S., et al. (2006) · Nonlinear Dynamics · doi:10.1007/s11071-006-1935-3 · Cited by 17
Design and implementation of a jerk circuit using a hybrid analog–digital system
Chiu, R., Lopez-Mancilla, D., Castaneda, C. E., et al. (2019) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2018.12.029 · Cited by 17
EXPERIMENTAL IMPROVEMENT OF CHAOTIC SYNCHRONIZATION DUE TO MULTIPLICATIVE TIME-CORRELATED GAUSSIAN NOISE
Pérez-Muñuzuri, V., & Lorenzo, M. N. (1998) · Cited by 17
Synchronization by dynamical relaying in electronic circuit arrays
Silva, I. G. D., Buldú, J. M., Mirasso, C. R., et al. (2006) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2374860 · Cited by 17
“In this paper we use a particular nonlinear electronic circuit, known as Chua’s circuit or double-scroll oscillator [7], which has become a paradigmatic example of chaotic circuit.”
Method
IMPULSIVE SYNCHRONIZATION OF CHAOTIC SYSTEMS VIA LINEAR MATRIX INEQUALITIES
JI, Y., Wen, C., & Li, Z. G. (2006) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127406014757 · Cited by 17
Analysis of irregular behaviour on an optical computing logic cell
Gonzalez-Marcos, A. P., & Martín-Pereda, J. A. (2000) · Optics & Laser Technology · doi:10.1016/s0030-3992(00)00099-2 · Cited by 17
“Chua's circuits are one of the most well-known studied case [8], In any of them, due to the characteristics of the initial conditions, signals were analogue.”
Background
QUALITATIVE RESONANCE OF SHIL'NIKOV-LIKE STRANGE ATTRACTORS, PART II: MATHEMATICAL ANALYSIS
Feo, O. D. (2004) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127404009739 · Cited by 17
Secure Digital Signal Transmission by Multistep Parameter Modulation and Alternative Driving of Transmitter VariablesPreprint
Palaniyandi, P., & Lakshmanan, M. (2001) · Cited by 17
Crisis induced intermittency in a fourth-order autonomous electric circuit
Stouboulos, I. N., Miliou, A. N., Valarıstos, A., et al. (2006) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2006.01.080 · Cited by 16
On computing Poincaré map by Hénon method
Palaniyandi, P. (2007) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2007.06.118 · Cited by 16
Dynamics of Hamiltonian Systems and Memristor Circuits
Itoh, M., & Chua, L. O. (2017) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127417300051 · Cited by 16
Spiking in Memristor Networks
Gale, E., Costello, B. D. L., & Adamatzky, A. (2013) · Springer eBooks · doi:10.1007/978-3-319-02630-5_17 · Cited by 16
The hyperbolicity problem in electrical circuit theory
Riaza, R., & Tischendorf, C. (2010) · Mathematical Methods in the Applied Sciences · doi:10.1002/mma.1312 · Cited by 16
Experimental network synchronization via plastic optical fiber
Arellano-Delgado, A., López-Gutiérrez, R. M., Cruz-Hernández, C., Posadas–Castillo, C., Cardoza-Avendaño, L., & Serrano-Guerrero, H. (2012) · Optical Fiber Technology · doi:10.1016/j.yofte.2012.11.007 · Cited by 16
Chaotic oscillator design and realizationsof the Rucklidge attractor and its synchronization and masking simulations
Pehli̇van, İ., Uyarolu, Y., & Youn, M. (2010) · Scientific Research and Essays · doi:10.5897/sre.9000259 · Cited by 16
“(Madan, 1993).”
An introduction to fractals and their applications in electrical engineering
Jacquin, A. E. (1994) · Journal of the Franklin Institute · doi:10.1016/0016-0032(94)90085-x · Cited by 16
Experimental study of high frequency stochastic resonance in Chua circuits
Gomes, I., Mirasso, C. R., Toral, R., et al. (2003) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(03)00461-8 · Cited by 16
MASTER-SLAVE SYNCHRONIZATION OF LUR'E SYSTEMS BASED ON TIME-VARYING DELAY FEEDBACK CONTROL
Huang, H., & Cao, J. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s021812740701969x · Cited by 16
“By Theorem 1, the master-slave synchronization scheme of Chua’s Circuit (14) is synchronous.”
Influential
HARMONIC BALANCE ANALYSIS OF THE GENERALIZED CHUA'S CIRCUIT
Savacı, F. A., & Günel, S. (2006) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127406016082 · Cited by 16
“Despite its minimal structure, it has a rich diversity of behaviors ranging from equilibrium states to period doubling bifurcations, from quasi-periodicity to intermittency which makes it a milestone in nonlinear research [Kennedy, 1993b, 1993c; Madan, 1993; Mira, 1997].”
BackgroundResult
CHAOS IN A NONLINEAR ANALOG COMPUTER
Kiers, K., KLEIN, T., Kolb, J., et al. (2004) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127404010898 · Cited by 16
“Such studies have been performed in the past using other chaotic systems, but not to the accuracy permitted by this system [Madan, 1993].”
Method
MODELING COMPLEX DYNAMICS VIA EXTENDED PWL-BASED CNNs
Fortuna, L., Rizzo, A., & Xibilia, M. G. (2003) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127403008727 · Cited by 16
ON GLOBAL EXPONENTIAL SYNCHRONIZATION OF CHUA CIRCUITS
Liao, X., Chen, G., Xu, B., et al. (2005) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127405013198 · Cited by 16
“…has been intensively studied in recent years [Pecora & Carroll, 1990, 1991; Hays et al., 1993; Wu & Chua, 1993, 1995, 1996; Ogorzalek, 1993; Madan, 1993; John & Amrithar, 1994; Yang & Yang, 1997; Chua et al., 1993; Liao, 1993; Chen & Dong, 1998; Lü & Chen, 2002; Liao et al., 2002; Liao &…”
MethodInfluential
HOPF BIFURCATIONS AND DEGENERACIES IN CHUA'S CIRCUIT — A PERSPECTIVE FROM A FREQUENCY DOMAIN APPROACH
Moiola, J. L., & Chua, L. O. (1999) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127499000171 · Cited by 16
Experimental study of high frequency stochastic resonance in Chua circuits
Gomes, I., Mirasso, C. R., Toral, R., et al. (n.d.) · RePEc: Research Papers in Economics · Cited by 16
THE ANALYSIS OF THE STOCHASTICALLY FORCED PERIODIC ATTRACTORS FOR CHUA'S CIRCUIT
RYAGIN, M. Y., & Ryashko, L. B. (2004) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127404011600 · Cited by 15
A New Chaotic Electro-Mechanical Oscillator
Buscarino, A., Famoso, C., Fortuna, L., et al. (2016) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127416501613 · Cited by 15
“…nonlinear circuits that are able to exhibit chaotic behavior: they can be intentionally designed to be chaotic as the paradigmatic Chua’s circuit [Madan, 1993; Fortuna et al., 2009], based on the properties of unique materials [Fortuna et al., 2006] or devices [Itoh & Chua, 2008; Muthuswamy,…”
Background
A double scroll based true random bit generator
Yalcin, M. E., Suykens, J. A. K., & Vandewalle, J. P. L. (2004) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.2004.1329070 · Cited by 14
“Since then, the double scroll attractor has been addressed by many researchers [4, 5].”
Background
Relaxation Oscillations in a Nonsmooth Oscillator with Slow-Varying External Excitation
Wang, Z., Zhang, Z., & Bi, Q. (2019) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127419300192 · Cited by 14
The Jerk Dynamics of Chua's Circuit
Buscarino, A., Fortuna, L., & Frasca, M. (2014) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127414500850 · Cited by 14
Chaos synchronization and transmission of information in coupled SC-CNN-based canonical Chua’s circuit
Swathy, P. S., Sabarathinam, S., Kumarasamy, S., et al. (2014) · Nonlinear Dynamics · doi:10.1007/s11071-014-1494-y · Cited by 14
“Motivation on the study of chaos synchronization, recently the possibility of synchronizing chaotic systems and its potential usefulness in communications with chaos and cryptography has attracted considerable interest [1–6] and a number of interesting methods have been proposed.”
BackgroundInfluential
Vibrational and Ghost-Vibrational Resonances in a Modified Chua's Circuit Model Equation
Karunanidhi, A., Rajasekar, S., & Sanjuán, M. A. F. (2014) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127414300316 · Cited by 14
“Over the past three decades the occurrence of different kinds of nonlinear phenomena in this circuit has been investigated experimentally, theoretically and numerically [Fortuna et al., 2009; Kilic, 2010; Madan, 1993].”
Background
GENERATION AND IMPLEMENTATION OF HYPERCHAOTIC CHUA SYSTEM VIA STATE FEEDBACK CONTROL
Xi, H., Yu, S., Zhang, C., et al. (2012) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127412501192 · Cited by 14
“Chua system is an ideal paradigm for research on chaos by means of both laboratory experiments and computer simulations [Matsumoto et al., 1985; Madan, 1993; Chua, 1994; Mira, 1997].”
Method
Spatio-temporal structures in ensembles of coupled chaotic systems
Strelkova, G. I., & Анищенко, В. С. (2019) · Physics-Uspekhi · doi:10.3367/ufne.2019.01.038518 · Cited by 14
“…˘˙ˇ(cid:209)—(cid:212)(cid:213)(cid:211)¸(cid:211)(cid:214)Æ(cid:213) (cid:215)¸˚¸(cid:218)˙(cid:212)˝¸˙ [150, 151], (cid:211)´˘¸(cid:209)(cid:224)˛˙˝(cid:213)-(cid:211)(cid:209)——(cid:222)˙ [130], (cid:216)¸ˇ¸(cid:218)˙(cid:212)˝¸˙ [152], ˆ¸(cid:209)˛(cid:209)¯¸(cid:218)˙(cid:212)˝¸˙ [153, 154] ·.”
Robust synchronization of chaotic systems subject to parameter uncertainties
Huang, H., Feng, G., & Sun, Y. (2009) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.3212940 · Cited by 14
Qualitative analysis of the dynamics of the time-delayed Chua's circuit
Biey, M., Bonani, F., Gilli, M., et al. (1997) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.586022 · Cited by 14
“As an example we report the simulations that refer to the case 0.49, 0.60, 0.78 and within the interval [ 4, 1].”
Influential
Impulse tuning of Chua chaos
Xu, W., Shen, H., Dai-ping, H., et al. (2005) · International Journal of Engineering Science · doi:10.1016/j.ijengsci.2004.08.008 · Cited by 14
A fuzzy approach for modeling chaotic dynamics with assigned properties
Porto, M., & Amato, P. (2002) · Proceedings of ... IEEE International Conference on Fuzzy Systems · doi:10.1109/fuzzy.2000.838699 · Cited by 14
Homoclinic orbits and solitary waves in a one-dimensional array of Chua's circuits
Nekorkin, V. I., Kazantsev, V., Rulkov, N. F., et al. (1995) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.473588 · Cited by 14
The Fractional Chua Chaotic System: Dynamics, Synchronization, and Application to Secure Communications
Bendoukha, S., & Abdelmalek, S. (2018) · International Journal of Nonlinear Sciences and Numerical Simulation · doi:10.1515/ijnsns-2018-0195 · Cited by 13
“Throughout the years, the Chuamodel (1) was studied extensively, see, for instance, [4, 5].”
Background
Global synchronization in lattices of coupled chaotic systems
Juang, J., Li, C.-L., & Liang, Y.-H. (2007) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2754668 · Cited by 13
Synchronous Chaos in Coupled Map Lattices with General Connectivity Topology
Juang, J., & Liang, Y.-H. (2008) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/070705179 · Cited by 13
DISCRETE CHAOTIC DYNAMICS FROM CHUA'S OSCILLATOR: CHUA MACHINES
Bilotta, E., & Pantano, P. (2009) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127409022774 · Cited by 13
CLASSIFICATION OF BIFURCATIONS AND CHAOS IN CHUA'S CIRCUIT WITH EFFECT OF DIFFERENT PERIODIC FORCES
Srinivasan, K., Thamilmaran, K., & Venkatesan, A. (2009) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127409023846 · Cited by 13
Controlling chaos in a memristor-based Chua's circuit
Zhang, J., Zhang, H., & Zhang, G. (2009) · International Conference on Communications, Circuits and Systems · doi:10.1109/icccas.2009.5250353 · Cited by 13
Stabilized chaotic dynamics of coupled nonisothermal CSTRs
Chen, C., Fu, C., & Tsai, C.-H. (1996) · Chemical Engineering Science · doi:10.1016/s0009-2509(96)00335-1 · Cited by 13
Intermittency in chaotic rotations
Lai, Y., Armbruster, D., & Kostelich, E. J. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.62.r29 · Cited by 13
Chaotic Systems Synchronization in Secure Communication Systems.
Harb, A., & Ahmad, W. (2006) · Cited by 12
Achieving criticality for reservoir computing using environment-induced explosive death
Mandal, S., & Shrimali, M. D. (2021) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0038881 · Cited by 12
Application of chaotic modulation to ac motors for harmonic suppression
Cui, W., Chau, K. T., Wang, Z., et al. (2006) · IEEE International Conference on Industrial Technology (ICIT) · doi:10.1109/icit.2006.372613 · Cited by 12
ADAPTIVE CONTROL AND SYNCHRONIZATION OF CHUA'S CIRCUITS
Liao, T., & Lin, S. (1999) · Asian Journal of Control · doi:10.1111/j.1934-6093.1999.tb00009.x · Cited by 12
Modular experimental setup for real‐time analysis of emergent behavior in networks of Chua's circuits
de Magistris, M., di Bernardo, M., Manfredi, S., et al. (2015) · International Journal of Circuit Theory and Applications · doi:10.1002/cta.2179 · Cited by 12
Rigorous Analysis of Chua’s Circuit With a Smooth Nonlinearity
Galias, Z. (2016) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2016.2613022 · Cited by 12
“Dynamical behaviors and the problem of existence of chaos in this system has been studied extensively since the invention of the circuit [3]–[6].”
Background
Neuromorphic computation with spiking memristors: habituation, experimental instantiation of logic gates and a novel sequence-sensitive perceptron model
Gale, E. (2018) · Faraday Discussions · doi:10.1039/c8fd00111a · Cited by 13
A NEW CLASS OF CHAOTIC ATTRACTORS IN MURALI–LAKSHMANAN–CHUA CIRCUIT
Oksasoglu, A., & Wang, Q. (2006) · International Journal of Bifurcation and Chaos · doi:10.1142/s021812740601632x · Cited by 12
A Noise Cleaning Method for Chaotic Time Series and Its Application in Communication
Feng, J. (2005) · Chinese Physics Letters · doi:10.1088/0256-307x/22/8/008 · Cited by 12
ANYONE CAN BUILD CHUA'S CIRCUIT: HANDS-ON-EXPERIENCE WITH CHAOS THEORY FOR HIGH SCHOOL STUDENTS
Gandhi, G., Cserey, G., ZBROZEK, J., et al. (2009) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127409023536 · Cited by 12
Robust Dichotomy Analysis and Synthesis With Application to an Extended Chua's Circuit
Yang, Y. Z., Duan, Z., & Huang, L. (2007) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/tcsi.2007.904670 · Cited by 12
“Taking , , , , , , the system with exact data has been studied in [21] and is known to have a chaotic attractor.”
Background
Experimental Characterization of Transition to Chaos in the Presence of Noise
Xu, B., Lai, Y., Zhu, L., et al. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.164101 · Cited by 12
“1, where 1(a) is the Chua’s circuit [19] and 1(b) is the noise divider that we design to obtain controllable noisy signals with fine resolution in amplitude from a commercial noise generator.”
Influential
Transformation and Equivalence
Mathis, W. M. (2018) · CRC Press eBooks · doi:10.1201/9781315219165-10 · Cited by 12
NONORGANIZED DETERMINISTIC DISSYMMETRIES INDUCE REGULARITY IN SPATIOTEMPORAL DYNAMICS
Arena, P., Caponetto, R., Fortuna, L., et al. (2000) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127400000049 · Cited by 12

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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