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Chua's Circuit: A Paradigm for Chaos
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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“Previously suggested chaotic circuits 19-22 , involving those with memristors 22 , involve several circuit elements.”
From Bistable Nonvolatile Elastic-Membrane Memcapacitor Exhibiting a Chaotic Behavior (2011) · cites this paper as [22]
In the citing paper
“Moreover, the membrane memcapacitor is a passive device in contrast with the active Chua's diode 21 and active memristors 22 used in existing chaotic circuits.”
From Bistable Nonvolatile Elastic-Membrane Memcapacitor Exhibiting a Chaotic Behavior (2011) · cites this paper as [22]
Citations
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Sorted by citations
Effects of noise in excitable systems
Lindner, B. (2004) · Physics Reports · doi:10.1016/j.physrep.2003.10.015 · Cited by 1,482
ITOH, M., & CHUA, L. O. (2008) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127408022354 · Cited by 1,020
Dedieu, H., Kennedy, M. P., & Hasler, M. (1993) · IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing · doi:10.1109/82.246164 · Cited by 829
Memory effects in complex materials and nanoscale systems
Pershin, Y. V., & Di Ventra, M. (2011) · Advances In Physics · doi:10.1080/00018732.2010.544961 · Cited by 823
“For the most part modified Chua’s oscillators [288,289] were considered [282,283,285,286].”
BackgroundHidden attractors in dynamical systems
Dudkowski, D., Jafari, S., Kapitaniak, T., Kuznetsov, N. V., Leonov, G. A., & Prasad, A. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.05.002 · Cited by 704
“where x, y and z are state variables and α, β, γ,m0 and m1 are constant [47].”
BackgroundKolumbán, G., Kennedy, M. P., & Chua, L. O. (1998) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.735435 · Cited by 435
Recurrent least squares support vector machines
Suykens, J. A. K., & Vandewalle, J. P. L. (2000) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.855471 · Cited by 341
Li, Z., Duan, Z., & Lewis, F. L. (2013) · Automatica · doi:10.1016/j.automatica.2013.12.008 · Cited by 322
“In this case, the leader displays a double-scroll chaotic attractor [34].”
BackgroundFAMILIES OF SCROLL GRID ATTRACTORS
Yalcin, M. E., Suykens, J. A. K., Vandewalle, J. P. L., et al. (2002) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127402004164 · Cited by 293
“Since the discovery of Chua’s circuit [Chua et al., 1986; Madan, 1993; Chua, 1994] many scientists from different disciplines have been studying the double scroll family.”
BackgroundLag synchronization in time-delayed systems
Shahverdiev, E. M., Sivaprakasam, S., & Shore, K. A. (2002) · Physics Letters A · doi:10.1016/s0375-9601(01)00824-6 · Cited by 286
True Random Bit Generation From a Double-Scroll Attractor
Yalcin, M. E., Suykens, J. A. K., & Vandewalle, J. P. L. (2004) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/tcsi.2004.830683 · Cited by 282
“Since then, the double-scroll attractor has been addressed by many researchers [28], [6].”
BackgroundChua, L. O., Hasler, M., Moschytz, G. S., & Neirynck, J. (1995) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.473564 · Cited by 274
Adaptive control and synchronization of a modified Chua's circuit system
Yassen, M. T. (2002) · Applied Mathematics and Computation · doi:10.1016/s0096-3003(01)00318-6 · Cited by 270
A chaotic circuit based on Hewlett-Packard memristor
Buscarino, A., Fortuna, L., Frasca, M., & Gambuzza, L. V. (2012) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4729135 · Cited by 254
Chaos synchronization of the Chua system with a fractional order
Li, C., Deng, W. H., & Xu, D. (2005) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2005.06.078 · Cited by 232
Experimental confirmation of 3- and 5-scroll attractors from a generalized Chua's circuit
Yalcin, M. E., Suykens, J. A. K., & Vandewalle, J. P. L. (2000) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.841929 · Cited by 183
“Existing circuit implementations of (1), (2) have been made for q = 1 corresponding to the double scroll case [12] and by Arena et al.”
BackgroundMethodInfluentialStability analysis and decentralized control of a class of complex dynamical networks
Duan, Z., Wang, J., Chen, G., et al. (2007) · Automatica · doi:10.1016/j.automatica.2007.08.005 · Cited by 182
Chua, L. O. (1999) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.739186 · Cited by 181
“However, if the nonlinear resistor is chosen to be a Chua’s diode [ 23 ], as shown in the inset in Fig. 2, then for the fixed choice of circuit parameters given in [22], the four distinctly different three-dimensional structures in Fig. 3 can be obtained in steady state by choosing the four different sets of initial c…”
MethodRobust synthesis for master-slave synchronization of Lur'e systems
Suykens, J. A. K., CURRAN, P. F., & Chua, L. O. (1999) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.774230 · Cited by 178
Robust nonlinear H/sub ∞/ synchronization of chaotic Lur'e systems
Suykens, J. A. K., CURRAN, P. F., Vandewalle, J. P. L., et al. (1997) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.633878 · Cited by 172
Does chaos work better than noise?
Bucolo, M. A. R., Caponetto, R., Fortuna, L., Frasca, M., & Rizzo, A. (2002) · IEEE Circuits and Systems Magazine · doi:10.1109/mcas.2002.1167624 · Cited by 171
“resistors (each circuit is characterized by parameters chosen according to [ 17 ] to generate the Double Scroll Chua Attractor) is taken into account, and both a random and a deterministic dissymmetry on a circuit parameter (the αk parameter is allowed to vary in a range of 10‐20% of its nominal value) are introduced.”
MethodInfluentialThree Types of Transitions to Phase Synchronization in Coupled Chaotic Oscillators
Osipov, G. V., Hu, B., Zhou, C., et al. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.024101 · Cited by 168
Synchronization of Chaotic Systems and Transmission of Information
Hasler, M. (1998) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127498000450 · Cited by 165
GENERALIZED SYNCHRONIZATION OF CHAOS VIA LINEAR TRANSFORMATIONS
Yang, T., & Chua, L. O. (1999) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127499000092 · Cited by 155
“A Chua’s circuit [Madan, 1993; Chua, 1994], which consists of two linear capacitors C1 and C2, a linear inductor L, two linear resistors R and R0, and a piecewise-linear negative resistor called a Chua’s diode, is described by the following state equation: dv1 dt = 1 C1 [G(v2 − v1)− f(v1)] dv2 dt =…”
BackgroundChua's circuit can be generated by CNN cells
Arena, P., Baglio, S., Fortuna, L., & Manganaro, G. (1995) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.372854 · Cited by 150
Synchronization of Chua’s circuits with multi-scroll attractors: Application to communication
Gámez-Guzmán, L., Cruz-Hernández, C., López-Gutiérrez, R. M., et al. (2008) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2008.10.009 · Cited by 149
An open-plus-closed-loop (OPCL) control of complex dynamic systems
Jackson, E. A., & Grosu, I. (1995) · Physica D Nonlinear Phenomena · doi:10.1016/0167-2789(95)00171-y · Cited by 146
Han, Q. (2007) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/tcsi.2007.899627 · Cited by 143
“and parameters , , , , and (Chua et al. [3]; Madan [ 15 ]).”
Chua, L. O. (1994) · International Journal of Circuit Theory and Applications · doi:10.1002/cta.4490220404 · Cited by 138
Control of imperfect dynamical systems
Bucolo, M., Buscarino, A., Famoso, C., et al. (2019) · Nonlinear Dynamics · doi:10.1007/s11071-019-05077-4 · Cited by 122
SYNTHESIS OF ELECTRONIC CIRCUITS FOR SIMULATING NONLINEAR DYNAMICS
Itoh, M. (2001) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127401002341 · Cited by 119
A GALLERY OF ATTRACTORS FROM SMOOTH CHUA'S EQUATION
Tsuneda, A. (2005) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127405011990 · Cited by 118
Persistent clusters in lattices of coupled nonidentical chaotic systems
Belykh, I. V., Белых, В. Н., Nevidin, K., & Hasler, M. (2003) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.1514202 · Cited by 114
PRINCIPLES OF CHAOTIC SIGNAL RADAR
Liu, Z., Zhu, X., Hu, W. S., et al. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127407018038 · Cited by 113
A linear continuous feedback control of Chua's circuit
Hwang, C., Jin-Yuan, H., & Rong-Syh, L. (1997) · Chaos Solitons & Fractals · doi:10.1016/s0960-0779(96)00150-6 · Cited by 112
Generalized connection graph method for synchronization in asymmetrical networks
Belykh, I. V., Белых, В. Н., & Hasler, M. (2006) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2006.09.014 · Cited by 111
Adaptive attack-free protocol for consensus tracking with pure relative output information
Lv, Y., Wen, G., Huang, T., et al. (2020) · Automatica · doi:10.1016/j.automatica.2020.108998 · Cited by 109
Cruz, J. M., & Chua, L. O. (1993) · IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing · doi:10.1109/82.246162 · Cited by 108
On simplifying and classifying piecewise-linear systems
Carmona, V., Freire, E., Ponce, E., et al. (2002) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/tcsi.2002.1001950 · Cited by 106
Synchronization in asymmetrically coupled networks with node balance
Belykh, I. V., Белых, В. Н., & Hasler, M. (2006) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2146180 · Cited by 103
BIFURCATION AND CHAOS IN THE FRACTIONAL-ORDER CHEN SYSTEM VIA A TIME-DOMAIN APPROACH
Cafagna, D., & Grassi, G. (2008) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127408021415 · Cited by 103
Chaos computing: implementation of fundamental logical gates by chaotic elements
Munakata, T., Sinha, S., & Ditto, W. L. (2002) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/tcsi.2002.804551 · Cited by 103
“For instance, chaotic electrical circuits have been extensively characterized and used for communications (see [21] for a review).”
BackgroundGeneration of $n\times m$-Wing Lorenz-Like Attractors From a Modified Shimizu–Morioka Model
Yu, S., Tang, K. S., Lü, J., et al. (2008) · IEEE Transactions on Circuits & Systems II Express Briefs · doi:10.1109/tcsii.2008.2002563 · Cited by 100
“On the other hand, extensive research has been performed on another typical chaotic system, Chua’s circuit [4], [5], and on the generation of attractors with multiscrolls or even a grid of scrolls [6]–[12].”
BackgroundCHUA’S EQUATION WITH CUBIC NONLINEARITY
Huang, A., Pivka, L., Wu, C. W., et al. (1996) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127496001454 · Cited by 99
“If in the original Chua's circuit we add a linear resistor in series with the inductor we obtain so-called Chua's oscillator [Madan, 1993].”
BackgroundMethodInfluentialA SYSTEMATIC APPROACH TO GENERATING N-SCROLL ATTRACTORS
Zhong, G., Man, K. F., & Chen, G. (2002) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127402006230 · Cited by 99
“Chua’s circuit Chua’s circuit is a simple autonomous system that can exhibit complex dynamics such as bifurcation and chaos [Zhong & Ayrom, 1985; Kennedy, 1992; Madan, 1993].”
BackgroundIdentifiability and identification of chaotic systems based on adaptive synchronization
Dedieu, H., & OGORZAŁEK, M. J. (1997) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.633884 · Cited by 92
Tse, K. K., Ng, R. W.-M., Chung, H. S.-H., & Hui, S. Y. R. (2003) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2002.807659 · Cited by 91
“The practical circuit of is shown in Fig. 3 [ 14 ], having dual operational amplifiers and six resistors (i.e., ). , , and are defined as follows:”
BackgroundChaotic pulse position modulation to improve the efficiency of sonar sensors
Fortuna, L., Frasca, M., & Rizzo, A. (2003) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2003.820452 · Cited by 91
A new chaotic secure communication system
Li, Z. G., Li, K., Wen, C., et al. (2003) · IEEE Transactions on Communications · doi:10.1109/tcomm.2003.815058 · Cited by 90
Mathematical Problems of Nonlinear Dynamics: A Tutorial
Shilnikov, L. P. (1997) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127497001527 · Cited by 89
Two-dimensional global manifolds of vector fields
Krauskopf, B., & Osinga, H. M. (1999) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.166450 · Cited by 89
Robust Nonlinear H Synchronization of Chaotic Lur'e Systems
Suykens, J. A. K., CURRAN, P. F., Vandewalle, J. P. L., et al. (1997) · Cited by 86
Turing patterns in CNNs. II. Equations and behaviors
Goraş, L., & Chua, L. O. (1995) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.473568 · Cited by 86
Coherence resonance in chaotic systems
Palenzuela, C., Toral, R., Mirasso, C. R., Calvo, O., & Gunton, J. D. (2001) · Europhysics Letters (EPL) · doi:10.1209/epl/i2001-00526-5 · Cited by 85
Impulsive control and synchronization of Chua’s oscillators
Sun, J., & Zhang, Y. (2004) · Mathematics and Computers in Simulation · doi:10.1016/j.matcom.2004.03.004 · Cited by 81
SPREAD SPECTRUM COMMUNICATION VIA CHAOS
Itoh, M. (1999) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127499000080 · Cited by 81
SLIDING MODE CONTROL OF CHAOS IN THE CUBIC CHUA'S CIRCUIT SYSTEM
Jang, M.-J., Chen, C., & Chen, C.-K. (2002) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127402005248 · Cited by 80
“Chua's circuit is a simple electronic circuit exhibiting a wide variety of chaotic phenomena [Madan, 1993].”
BackgroundImplementation of NOR Gate by a Chaotic Chua's Circuit
Murali, K., Sinha, S., & Ditto, W. L. (2003) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127403008053 · Cited by 80
“The dynamics of Chua’s circuit can be represented by the following set of (rescaled) three-coupled ODE’s [Madan, 1993; Lakshmanan & Murali, 1996] dx1 dt = α(x2 − x1 − h(x1)) , dx2 dt = x1 − x2 + x3 , dx3 dt = −βx2 , (1) Fig.2.”
Deng, W., & Lü, J. (2007) · Physics Letters A · doi:10.1016/j.physleta.2007.04.112 · Cited by 80
“Df”
GENERATION OF n × m-SCROLL ATTRACTORS UNDER A CHUA-CIRCUIT FRAMEWORK
Yu, S., Tang, K. S., & Chen, G. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127407019809 · Cited by 79
“Its rich variety of bifurcations and chaos arouse a great deal of interest [Kennedy, 1993; Madan, 1993; Wu, 1987].”
BackgroundCafagna, D., & Grassi, G. (2008) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127408020550 · Cited by 79
“By considering that the well-known integer order Chua’s circuit is widely considered a paradigm for chaos [Chua et al., 1986; Madan, 1993; Chua, 1994], in this tutorial, attention is focused on the fractional-order Chua’s circuit.”
Chaotic cryptosystem with high sensitivity to parameter mismatch
Li, K., Soh, Y. C., & Li, Z. G. (2003) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/tcsi.2003.809808 · Cited by 78
“Just as in [17], we let k = 1, m0 = 01:138411196, m1 = 00:722451121, and = 9:351590850, = 14:790313805, = 0:016073965.”
On the synchronization of a class of electronic circuits that exhibit chaos
Bai, E., Lonngren, K. E., & Sprott, J. C. (2002) · Chaos Solitons & Fractals · doi:10.1016/s0960-0779(01)00160-6 · Cited by 78
Robust interval observers for global Lipschitz uncertain chaotic systems
Moisan, M., & Olivier Bernard, A. (2010) · Systems & Control Letters · doi:10.1016/j.sysconle.2010.08.005 · Cited by 77
Control of Chaos Using Sampled-Data Feedback Control
Yang, T. (1998) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127498001947 · Cited by 77
“In this example, we use Chua’s oscillator [Madan, 1993], which is shown in Fig.”
MethodDeng, W., & Lü, J. (2006) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2401061 · Cited by 75
Hyperchaos from cellular neural networks
Arena, P., Baglio, S., Fortuna, L., et al. (1995) · Electronics Letters · doi:10.1049/el:19950189 · Cited by 74
Bucolo, M., Buscarino, A., Famoso, C., et al. (2021) · IEEE Access · doi:10.1109/access.2021.3058506 · Cited by 73
“We focus, therefore, on two different off-the-shelf integrated circuits, the LM311p and the TL084, whose realization is connected to unavoidable manufacturing imperfections with respect to the ideal model, which are the key ingredients to observe unexpected chaotic oscillations with a bandwidth up to several megahertz…”
Synchronizing hyperchaotic systems by observer design
Grassi, G., & Mascoio, S. (1999) · IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing · doi:10.1109/82.755422 · Cited by 73
“For this reason, chaotic dynamics, synchronization of coupled dynamic systems, and secure communications have been the topics of many papers over the last few years [1]–[7].”
BackgroundEmulating complex business cycles by using an electronic analogue
Bouali, S., Buscarino, A., Fortuna, L., Frasca, M., & Gambuzza, L. V. (2012) · Nonlinear Analysis Real World Applications · doi:10.1016/j.nonrwa.2012.02.010 · Cited by 72
“Examples of chaotic circuits exploiting the specific features of some electronic components are the Chua circuit [17] using a nonlinear component with piecewise linear characteristic, the circuits reported in [18–20] based on hysteretic elements and the circuits based on memristors discussed in [21–24], while switchin…”
BackgroundMethodGenerating 2n‐wing attractors from Lorenz‐like systems
Yu, S., Tang, K. S., Lü, J., et al. (2008) · International Journal of Circuit Theory and Applications · doi:10.1002/cta.558 · Cited by 70
“In contrast, various multi-scroll attractors under the framework of Chua’s circuit [11, 12] and some similar forms have been extensively studied, which can be generated by using many different non-linear functions [13–38], such as multi-segment piecewise-linear [13, 14, 18], trigonometric [27], hyperbolic [33, 38], hy…”
BackgroundTuring patterns in CNNs. I. Once over lightly
Goraş, L., Chua, L. O., & Leenaerts, D. M. W. (1995) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.473567 · Cited by 69
Cancellable face recognition based on fractional-order Lorenz chaotic system and Haar wavelet fusion
Badr, I. S., Radwan, A. G., El‐Rabaie, E. M., Said, L. A., El‐Banby, G. M., El‐Shafai, W., & El‐Samie, F. E. A. (2021) · Digital Signal Processing · doi:10.1016/j.dsp.2021.103103 · Cited by 68
A new feedback control of a modified Chua's circuit system
Hwang, C., Chow, H.-Y., & Wang, Y.-K. (1996) · Physica D Nonlinear Phenomena · doi:10.1016/0167-2789(95)00276-6 · Cited by 67
“Chua's circuit, suggested by L.O. Chua, has been studied extensively as a prototypical electronic system [11].”
BackgroundOwolabi, K. M., & Atangana, A. (2017) · Computational and Applied Mathematics · doi:10.1007/s40314-017-0445-x · Cited by 66
STAR CELLULAR NEURAL NETWORKS FOR ASSOCIATIVE AND DYNAMIC MEMORIES
Itoh, M., & Chua, L. O. (2004) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127404010308 · Cited by 64
“…0 ∂g(x 0 , y 0 , z 0 ) ∂x 0 ∂g(x 0 , y 0 , z 0 ) ∂y 0 ∂g(x 0 , y 0 , z 0 ) ∂z 0 ∂h(x 0 , y 0 , z 0 ) ∂x 0 ∂h(x 0 , y 0 , z 0 ) ∂y 0 ∂h(x 0 , y 0 , z 0 ) ∂z 0 × ∆x ∆y ∆z (52) where ∆x = x i − x 0 , ∆y = y i − y 0 , ∆z = z i − z 0 (for more details, see [Madan, 1993]).”
BackgroundMethodInfluentialA GALLERY OF CHUA ATTRACTORS PART V
Bilotta, E., Blasi, G. D., STRANGES, F., et al. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127407018099 · Cited by 64
Chaos control of the modified Chua’s circuit system
Wu, T., & Chen, M. (2002) · Physica D Nonlinear Phenomena · doi:10.1016/s0167-2789(02)00360-3 · Cited by 64
“PACS:05.45.+b Keywords:Chaos control; Chua’s circuit; Nonlinear control; Backstepping control”
InfluentialToward nonlinear wave digital filters
Sarti, A., & Poli, G. D. (1999) · IEEE Transactions on Signal Processing · doi:10.1109/78.765137 · Cited by 63
Hyperchaotic Coupled Chua Circuits: An Approach for Generating New n×m-Scroll Attractors
Cafagna, D., & Grassi, G. (2003) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127403008065 · Cited by 62
“In particular, several researchers have focused their attention on Chua’s circuit, which is the most extensively studied chaotic electrical system [Madan, 1993].”
BackgroundBistable Nonvolatile Elastic-Membrane Memcapacitor Exhibiting a Chaotic Behavior
Martinez-Rincon, J., & Pershin, Y. V. (2011) · IEEE Transactions on Electron Devices · doi:10.1109/ted.2011.2126022 · Cited by 68
“Moreover, the membrane memcapacitor is a passive device in contrast with the active Chua’s diode [21] and the”
BackgroundCorrelation analysis of dynamical chaos
Анищенко, В. С., Вадивасова, Т. Е., Okrokvertskhov, G., & Strelkova, G. I. (2003) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(03)00199-7 · Cited by 59
Fault-Tolerant Master–Slave Synchronization for Lur'e Systems Using Time-Delay Feedback Control
Zhong, M., & Han, Q. (2008) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2008.2006218 · Cited by 59
“When a fault is taken into account, Chua’s circuit in [5] and [ 20 ] becomes”
BackgroundEXPERIMENTAL STUDY OF IMPULSIVE SYNCHRONIZATION OF CHAOTIC AND HYPERCHAOTIC CIRCUITS
Itoh, M., Yang, T., & Chua, L. O. (1999) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127499000961 · Cited by 58
“The dynamics of Chua’s oscillator [Madan, 1993], whose block diagram is shown in Fig.”
BackgroundSynchronization Analysis of Coupled Noncoherent Oscillators
Kurths, J., Romano, M. C., Marco Thiel, A., et al. (2006) · Nonlinear Dynamics · doi:10.1007/s11071-006-1957-x · Cited by 57
Emelianova, Y. P., Кузнецов, А. П., Sataev, I. R., et al. (2012) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2012.10.012 · Cited by 55
“Such models as Brusselator [10-11] and electronic oscillators [3,15-18] are also widely investigated.”
BackgroundA FAST AND SIMPLE IMPLEMENTATION OF CHUA'S OSCILLATOR WITH CUBIC-LIKE NONLINEARITY
O'DONOGHUE, K., Kennedy, M. P., FORBES, P., et al. (2005) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127405013800 · Cited by 55
CLUSTER SYNCHRONIZATION IN THREE-DIMENSIONAL LATTICES OF DIFFUSIVELY COUPLED OSCILLATORS
Белых, В. Н., Belykh, I. V., Hasler, M., et al. (2003) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127403006923 · Cited by 55
“This form of the function f(x) and the corresponding parameter values are chosen to lead the system (24) to a form of the generalized Chua circuit [Madan, 1993] and to provide the existence of a double-scroll attractor defining the chaotic behavior of the individual oscillator of the lattice.”
BackgroundFotsin, H. B., Bowong, S., & Daafouz, J. (2005) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2004.12.029 · Cited by 54
Chua's circuit decomposition: a systematic design approach for chaotic oscillators
Elwakil, A. S., & Kennedy, M. P. (2000) · Journal of the Franklin Institute · doi:10.1016/s0016-0032(00)00019-3 · Cited by 54
Experimental Observation of Superpersistent Chaotic Transients
Zhu, L., Raghu, A., & Lai, Y.-C. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.4017 · Cited by 54
A GALLERY OF CHUA ATTRACTORS: PART I
Bilotta, E., Pantano, P., & STRANGES, F. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127407017161 · Cited by 53
Driscoll, T., Pershin, Y. V., Basov, D. N., & Ventra, M. D. (2011) · Applied Physics A · doi:10.1007/s00339-011-6318-z · Cited by 54
“This approach to chaos with memristors is unique and radically different from previous proposals [22, 28–30] that are based on modified Chua’s circuits [31, 32] with active elements.”
ResultControlling chaos in a switched arrival system
Ushio, T., Ueda, H., & HIRAI, K. (1995) · Systems & Control Letters · doi:10.1016/0167-6911(95)00032-1 · Cited by 52
Zhao, Y., Zhou, Y., Huang, P., & Chen, G. (2022) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2022.3159558 · Cited by 51
“AlthoughAssumption 3issomewhatstrict,therearepracticalexamplessatisfyingthese conditions,suchasthird-orderChua’scircuitintroducedin[49], transportaircraftsembeddedshort-perioddynamicsaddressed in [50], and rotary-wing air vehicles studied in [51].”
BackgroundItoh, M., & Chua, L. O. (2013) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127413300012 · Cited by 51
“We first study the circuit equation of Chua’s circuit [Madan, 1993].”
MethodChua's oscillator: A compendium of chaotic phenomena
Pivka, L., Wu, C. W., & Huang, A. (1994) · Journal of the Franklin Institute · doi:10.1016/0016-0032(94)90087-6 · Cited by 51
Nonlinear H/sub ∞/ synchronization of Lur'e systems: dynamic output feedback case
Suykens, J. A. K., CURRAN, P. F., Yang, T., et al. (1997) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.641776 · Cited by 50
Dynamics of Memristor Circuits
Itoh, M., & Chua, L. O. (2014) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127414300158 · Cited by 48
“(140) can be recast into Hamilton’s equations Hamilton’s equations of memristor circuits dx dτ = ∂H(x, i) ∂i = Lf(i) i , di dτ = −∂H(x, i) ∂y = −M(x) g(x) , (141) where g(x)i = 0 and Hamiltonian of memristor circuits H(x, i) = ∫ Lf(i) i di + ∫ M(x) g(x) dx, (142) which have a solution H(x, i) = H0 (H0 is any constant)…”
BackgroundInfluentialWang, C., Ma, J., Liu, Y., & Huang, L. (2011) · Nonlinear Dynamics · doi:10.1007/s11071-011-9965-x · Cited by 49
“Clearly, the original Chua circuit [5] is a class of realistic model to be investigated.”
Background
Metadata
- 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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