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 301–400 of 598

Models of complex dynamics in nonlinear systems
GENESIO, R., Tesi, A., & Villoresi, F. (1995) · Systems & Control Letters · doi:10.1016/0167-6911(94)00070-c · Cited by 12
Computation and convergence of fixed-point with an RLC-electric circuit model in an extended b-suprametric space
Panda, S. K., Vijayakumar, V., Khan, I., et al. (2024) · Scientific Reports · doi:10.1038/s41598-024-59859-x · Cited by 11
Robustness to noise in synchronization of network motifs: Experimental results
Buscarino, A., Fortuna, L., Frasca, M., et al. (2012) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4761962 · Cited by 11
On the modeling and nonlinear dynamics of autonomous Silva-Young type chaotic oscillators with flat power spectrum
Kengne, J., & Kenmogné, F. (2014) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4903313 · Cited by 11
Arbitrary observer scaling of all chaotic drive system states via a scalar synchronizing signal
Grassi, G., & MILLER, D. A. (2007) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2007.06.002 · Cited by 11
Chasing chaos by improved identification of suitable embedding dimensions and lags
Perinelli, A., & Ricci, L. (2020) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0029333 · Cited by 11
Analysis of a Belyakov homoclinic connection with ℤ2-symmetry
Algaba, A., Merino, M., & Rodríguez-Luis, A. J. (2011) · Nonlinear Dynamics · doi:10.1007/s11071-011-0283-0 · Cited by 11
Effect of smoothing on robust chaos
Deshpande, A., Chen, Q., Wang, Y., et al. (2010) · Physical Review E · doi:10.1103/physreve.82.026209 · Cited by 11
Cluster Synchronization of Nonlinearly Coupled Complex Networks via Pinning Control
Feng, J., Wang, J., Xu, C. G., et al. (2011) · Discrete Dynamics in Nature and Society · doi:10.1155/2011/262349 · Cited by 11
Simplified scheme for realisation ofChua oscillator by using SC-CNN cells
Arena, P., Baglio, S., Fortuna, L., et al. (1995) · Electronics Letters · doi:10.1049/el:19951235 · Cited by 11
HYPERCHAOS IN A CHUA'S CIRCUIT WITH TWO NEW ADDED BRANCHES
Barboza, R. (2008) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127408020884 · Cited by 11
“Chua’s circuit is one of the best known and studied physical systems displaying chaotic behavior (see, e.g. [Madan, 1993; Chua, 1994; Mira, 1997]).”
Background
Experimental Chua's circuit arrays as an autowave simulator
Gómez-Gesteira, M., deCastro, M., Pérez-Villar, V., et al. (1999) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.754851 · Cited by 11
Chua's Circuit in Spread Spectrum Communication Systems
Galajda, P., & Kocur, D. (2002) · Brno University of Technology Digital Library (Brno University of Technology) · Cited by 10
Exploring an experimental analog Chua’s circuit
Prebianca, F., Marcôndes, D. W. C., Albuquerque, H. A., et al. (2019) · The European Physical Journal B · doi:10.1140/epjb/e2019-100097-4 · Cited by 10
“To compare the experimental results of the analog computer of Figure 1, we also carry out numerical simulations of the model (1)–(3) using the canonical nonlinearity (4) and a cubic function given by”
BackgroundMethodInfluential
A proof of Euzébio–Pazim–Ponce’s conjectures for a degenerate planar piecewise linear differential system with three zones
Chen, H., & Tang, Y. (2019) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2019.132150 · Cited by 10
Stability analysis for the Chua circuit with cubic polynomial nonlinearity based on root locus technique and describing function method
Rocha, R., & Medrano-T, R. O. (2020) · Nonlinear Dynamics · doi:10.1007/s11071-020-06039-x · Cited by 10
Structural characterization of classical and memristive circuits with purely imaginary eigenvalues
Riaza, R., & Tischendorf, C. (2011) · International Journal of Circuit Theory and Applications · doi:10.1002/cta.798 · Cited by 10
“Qualitative results are related, for example, to the stability properties of equilibria and operating points [5,17,22,28,60], oscillations [11,21,25,44], bifurcations [15,42,55], or chaotic phenomena [3,19,31,34,35,38,40,41,63,65].”
Background
Rank one chaos in a switch-controlled Chua's circuit
Oksasoglu, A., & Wang, Q. (2010) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2010.06.006 · Cited by 10
Isolas, cusps and global bifurcations in an electronic oscillator
Fernández-Sánchez, F., Freire, E., & Rodríguez-Luis, A. J. (1997) · Dynamics and Stability of Systems · doi:10.1080/02681119708806250 · Cited by 10
Global Dynamics of Memristor Oscillator
Chen, H. (2016) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127416501984 · Cited by 10
“…physicists and engineers have been interested in memristor oscillators, see [Borghetti et al., 2010; Chua, 1971; Chua & Kang, 1976; Itoh & Chua, 2008; Llibre et al., 2015; Llibre & Teruel, 2014; Madan, 1993; Raja & Mourad, 2010; Williams, 2008; Yang et al., 2008] and the references therein.”
Background
Effect of common noise on phase synchronization in coupled chaotic oscillators
Park, K., Lai, Y., Krishnamoorthy, S., et al. (2007) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2424423 · Cited by 10
The K.U.Leuven competition data : a challenge for advanced neural network techniques
Suykens, J. A. K., & Vandewalle, J. P. L. (2000) · Cited by 10
Bistable phase control via rocking in a nonlinear electronic oscillator
Buldú, J. M., Staliūnas, K., Casals, J. A., et al. (2006) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2404776 · Cited by 10
“Our nonlinear electronic oscillator is the so-called Chua circuit, which is a simple electronic circuit widely used for the generation of low dimensional chaotic regimes [6].”
Background
MECHANICAL MODELS OF CHUA'S CIRCUIT
Awrejcewicz, J., & Calvisi, M. L. (2002) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127402004668 · Cited by 10
“The unfolding of Chua’s circuit can exhibit various chaotic and bifurcation behaviors which are welldocumented in the literature [Madan, 1993].”
Background
EXPERIMENTAL DEFINITION OF THE BASIN OF ATTRACTION FOR CHUA'S CIRCUIT
Pegna, G. G., MARROCU, R., Tonelli, R., et al. (2000) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127400000682 · Cited by 10
“Universal because all characteristic features of chaotic motion (like period- doubling, intermittency, torus breakdown, etc.) have all been observed in this circuit [Madan, 1993].”
BackgroundInfluential
Output feedback form of Chua’s circuit and modular adaptive control of chaos using single measurement
Maganti, G. B., & Singh, S. N. (2005) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2005.08.139 · Cited by 10
Attraction/repulsion functions in a new class of chaotic systems
Duan, Z., Wang, J., & Huang, L. (2004) · Physics Letters A · doi:10.1016/j.physleta.2004.11.056 · Cited by 10
The evolution of spatio-temporal disorder in a chain of unidirectionally-coupled Chua's circuits
Osipov, G. V., & Shalfeev, V. D. (1995) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.473575 · Cited by 10
MOSFET-only Meminductor Emulator and its Application in Chaotic Oscillator
Kumar, A., & Rai, S. K. (2024) · Circuits Systems and Signal Processing · doi:10.1007/s00034-024-02833-9 · Cited by 9
“Among the tools used for studying and inducing chaos in electronic and communication systems, Chua’s chaotic oscillator [22, 30] stands out.”
Synchronizability of directed networks: The power of non-existent ties
Daley, K., Zhao, K., & Belykh, I. V. (2020) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.5134920 · Cited by 9
CHUA SYSTEMS WITH DISCONTINUITIES
Lamarque, C., Janin, O., & Awrejcewicz, J. (1999) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127499000420 · Cited by 9
“At the same time a number of papers deal with “simpler, integrable” systems which seem to be “paradigms”: Unimodal maps [Collet & Eckmann, 1980; Li & Yorke, 1975; Sharkovski, 1964], Lozi’s attractor [Lozi, 1978], Chua’s double scroll circuit [Madan, 1993], etc.”
Chaos Control of Uncertain Chaotic Systems via Backstepping Approach
Bowong, S., & Kakmeni, F. M. M. (2005) · Journal of vibration and acoustics · doi:10.1115/1.2110864 · Cited by 9
SYNCHRONIZING CHAOTIC ATTRACTORS OF CHUA'S CANONICAL CIRCUIT: THE CASE OF UNCERTAINTY IN CHAOS SYNCHRONIZATION
Kyprianidis, I. M., BOGIATZI, A. N., Papadopoulou, M. S., et al. (2006) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127406015829 · Cited by 9
“Chua’s circuit is a paradigm for chaos [Madan, 1993].”
Background
A chaotic modulation scheme based on algebraic observability and sliding mode differentiators
Cannas, B., Cincotti, S., & Usai, E. (2005) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2004.12.035 · Cited by 9
Secure Communications Based on Variable Topology of Chaotic Circuits
Alexeyev, A. A., & Green, M. M. (1997) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127497001941 · Cited by 9
Stable Synchrony in Globally Coupled Integrate-and-Fire Oscillators
Chang, Y., & Juang, J. (2008) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/070709220 · Cited by 8
Encryption Using Two Non-Identical Chaotic Systems
Cai, T., Cai, T., Zhou, C., & Yu, M. Y. (2002) · Physica Scripta · doi:10.1238/physica.regular.066a00187 · Cited by 9
“(6) is decoupled from the remaining equations and the LS equations become equivalent to the Lorenz equations.”
BackgroundInfluential
High Order Chua's Circuit and Its FPGA Realization
Yu, S., & Lü, J. (2006) · Chinese Control Conference (CCC) · doi:10.1109/chicc.2006.4347394 · Cited by 9
“目前,大多数文献主要集中在用模拟电路产生混沌信号([1-12]),本节进一步研究了用 FPGA 技术产生模拟混沌信号。最近, Caponetto 等报道了用 FPAA(Field Programmable Analog Array)产生模拟混沌信号,而用 FPGA(Field Programmable Gate Array) 等数字信号处理技术产生连续时间混沌信号的相关报道却很少,主要原因是技术上存在困难([6])。由于数字信号处理技术都是针对离散系统的,因此,必须对连续时间混沌系统作离散化处理后,才能应用 FPGA 的硬件实现。本实验中所使用的软件开发平台是 ALTERA 公司开发的 QUARTUS II 5.”
Oscillations and their mechanism of compound system with periodic switches between two subsystems
Yu, Y., Zhang, C., Han, X., et al. (2012) · Acta Physica Sinica · doi:10.7498/aps.61.200507 · Cited by 8
A review of chaotic circuits, simulation and implementation
Aissi, C., & Kazakos, D. (2006) · Cited by 8
Network Synchronization of MACM Circuits and Its Application to Secure Communications
Méndez-Ramírez, R. D., Arellano-Delgado, A., & Murillo-Escobar, M. A. (2023) · Entropy · doi:10.3390/e25040688 · Cited by 8
Advantages of the linz-sprott weak nonlinearity on the FPGA implementation of chaotic systems: a comparative analysis
Indrusiak, L. S., Silva, É. C. D. E., & Glesner, M. (2006) · International Symposium on Signals, Circuits and Systems · doi:10.1109/isscs.2005.1511350 · Cited by 8
ESTIMATING ERROR GROWTH AND SHADOW BEHAVIOR IN NONLINEAR DYNAMICAL SYSTEMS
Orrell, D. (2005) · International Journal of Bifurcation and Chaos · doi:10.1142/s021812740501409x · Cited by 8
“The lower panels show errors for the Chua circuit (Madan, 1993; Matsumoto et al., 1985), where the model is given by Eqs.”
Background
On the study of cellular nonlinear networks via amplitude and phase dynamics
Lanza, V., Corinto, F., & Gilli, M. (2007) · Neural Networks · doi:10.1016/j.neunet.2007.12.015 · Cited by 8
CHAOTIC PHASE SYNCHRONIZATION BASED ON BINARY COUPLING SIGNALS
Parlitz, U., & Wedekind, I. (2000) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127400001687 · Cited by 8
“…experiments as those described in the previous section have also been performed with two almost identical unidirectionally coupled Chua's circuits [Madan, 1993; Kocarev & Parlitz, 1995] C 1 dV C1 dt = G(V C2 − V C1 ) − f (V C1 ) C 2 dV C2 dt = G(V C1 − V C2 ) + I L (6) L dI L dt = V C2 and C 1 d…”
Random shortcuts induce phase synchronization in complex Chua systems
Du-Qu, W., Xiao-Shu, L., & Qin, Y.-H. (2009) · Chinese Physics B · doi:10.1088/1674-1056/18/6/012 · Cited by 8
Analysis of oscillation and stability for systems with piecewise linear components via saturation functions
Hu, T., Thibodeau, T., & Teel, A. R. (2009) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2009.5160519 · Cited by 8
“,limit cycle and chaotic oscillation) can be realized with Chua’s circuit family [17], [23], a class of third-order circuits with four linear elements and a piecewise linear resistive element (usually with two breakpoints in [0,∞], see Fig.”
Background
Rigorous integration of smooth vector fields around spiral saddles with an application to the cubic Chua's attractor
Galias, Z., & Tucker, W. (2018) · Journal of Differential Equations · doi:10.1016/j.jde.2018.08.035 · Cited by 8
STATISTICAL MEASURES AND DIFFUSION DYNAMICS IN A MODIFIED CHUA'S CIRCUIT EQUATION WITH MULTISCROLL ATTRACTORS
Sakthivel, G., Rajasekar, S., Thamilmaran, K., et al. (2012) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127412500046 · Cited by 8
“Chua’s circuit is found to show a rich variety of both local and global bifurcations and various types of chaotic orbits [Madan, 1993; Tsuneda, 2005; Bilotta et al., 2007].”
Background
Analytical studies on the dynamics of higher-dimensional nonlinear circuit systems
Sivaganesh, G., Srinivasan, K., & Arulgnanam, A. (2022) · Pramana · doi:10.1007/s12043-022-02428-6 · Cited by 8
Chua's circuit and the qualitative theory of dynamical systems
Mira, C. (1997) · Journal of the Franklin Institute · doi:10.1016/s0016-0032(97)00046-x · Cited by 8
“The important book by Madan [1993] collects many contributions devoted to applied and theoretical questions related to this circuit, which since this publication has given rise to many new developments.”
Background
GRAPH-THEORETIC CHARACTERIZATION OF BIFURCATION PHENOMENA IN ELECTRICAL CIRCUIT DYNAMICS
Riaza, R. (2010) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127410025533 · Cited by 8
Parameter estimation for random dynamical systems using slice sampling
Hatjispyros, S. J., Nicoleris, T., & Walker, S. G. (2007) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2007.03.013 · Cited by 8
“For instance, as a simple model for turbulence [1], to understand the behaviour of plasmas [2] and the origin of kinetic theory in statistical mechanics [3,4], in modelling the behaviour of nonlinear electronic circuits [18], etc.”
CHAOTIC BEATS IN A MODIFIED CHUA'S CIRCUIT: DYNAMIC BEHAVIOR AND CIRCUIT DESIGN
Cafagna, D., & Grassi, G. (2004) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127404011181 · Cited by 8
An experimental setup for studying the effect of noise on Chua's circuit
Sanchez, E., Matı́as, M. A., & Pérez-Muñuzuri, V. (1999) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.754855 · Cited by 8
“Our experiments are based on Chua’s circuit, a well-known paradigm of nonlinear analog circuits exhibiting chaotic behavior [7].”
Chaos control by using Motor Maps
Arena, P., Fortuna, L., & Frasca, M. (2002) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.1487615 · Cited by 8
Fully Distributed Adaptive Output Feedback Protocols for Linear Multi-Agent Systems with Directed Graphs: A Sequential Observer Design ApproachPreprint
Lv, Y., Li, Z., Duan, Z., & Chen, J. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1511.01297 · Cited by 9
SYNCHRONIZATION OF CHAOTIC SYSTEMS WITH PARAMETRIC UNCERTAINTY AND MISMATCH
Wen, C., JI, Y., Soh, Y. C., et al. (2006) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127406015416 · Cited by 8
“Chua’s circuit The Chua’s circuit [Madan, 1993] with parametric perturbation is given by: dx dt = (α + ∆α)(y − x − (f(x) + ∆f(x))) dy dt = x − y + z dz dt = −(β + ∆β)y − (γ + ∆γ)z (8) where f(x) = bx + (1/2)(a − b){|x + 1| − |x − 1|}, ∆f(x) = ∆bx + (1/2)(∆a − ∆b){|x + 1| − |x − 1|}. a, b, α, β…”
Controlling chaos in electronic circuits
OGORZAŁEK, M. J. (1995) · Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences · doi:10.1098/rsta.1995.0095 · Cited by 8
Controlling chaotic and hyperchaotic systems via energy regulation
Laval, L., & M’Sirdi, N. K. (2003) · Chaos Solitons & Fractals · doi:10.1016/s0960-0779(03)00470-3 · Cited by 8
FREQUENCY DOMAIN METHOD FOR THE DICHOTOMY OF MODIFIED CHUA'S EQUATIONS
Duan, Z., Wang, J., & Huang, L. (2005) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127405013435 · Cited by 8
“The study of Chaotic attractors has attracted a lot of researchers since Lorenz presented a simple three-dimensional chaotic system, see [Celikovski & Chen, 2002; Chua, 1994; Lorenz, 1963; Madan, 1993; Shil’nikov, 1993] and references therein.”
BackgroundMethodInfluential
A novel Chua’s based 2–D chaotic system and its performance analysis in cryptography
Rasappan, S., Kumaravel, S., Sambas, A., Moghrabi, I., Sulaiman, I., & Hassan, B. A. (2024) · PLoS ONE · doi:10.1371/journal.pone.0306818 · Cited by 6
LMI-Based Synchronization of Fractional-Order Chaotic Lur’e System with Control Input Delay using Guaranteed Cost Control Approach
Aghayan, Z. S., & Alfi, A. (2022) · Iranian Journal of Science and Technology Transactions of Electrical Engineering · doi:10.1007/s40998-022-00554-w · Cited by 7
“…some nonlinear systems, such as hyper chaotic attractors Kapitaniak and Chua (1994), N-scroll attractors Yalcin et al. (2000), and Chua’s circuit Madan (1993), are exactly represented as Lur’e control system, M-S of LSs is a problem under strong development in both theory and application Duan…”
Background
Chaos preservation through continuous chaotic pulse position modulation
Fortuna, L., Frasca, M., & Rizzo, A. (2002) · doi:10.1109/iscas.2001.921454 · Cited by 7
A Bayesian nonparametric study of a dynamic nonlinear model
Hatjispyros, S. J., Nicoleris, T., & Walker, S. G. (2009) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2009.05.009 · Cited by 7
A GENERALIZATION OF SMOOTH CHUA'S EQUATIONS UNDER LAGRANGE STABILITY
Duan, Z., Wang, J., Li, R., et al. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127407018853 · Cited by 7
“International Journal of Bifurcation and Chaos, Vol. 17, No. 9 (2007) 3047–3059 c© World Scientific Publishing Company A GENERALIZATION OF SMOOTH CHUA’S EQUATIONS UNDER LAGRANGE STABILITY* ZHISHENG DUAN†, JINZHI WANG, RONG LI and LIN HUANG State Key Laboratory for Turbulence and Complex Systems and Department of Mecha…”
Background
A NOTE ON A PIECEWISE-LINEAR DUFFING-TYPE SYSTEM
Tigan, G., & Astolfi, A. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127407020087 · Cited by 7
“In fact, Chua and collaborators discovered chaotic behavior in piecewise linear systems [9].”
Background
Extended chaos control method applied toChua circuit
rres, L. A. B. T., & Aguirre, L. A. (1999) · Electronics Letters · doi:10.1049/el:19990560 · Cited by 7
Mathematical Analysis of Memristor CNN
Slavova, A., & Tetzlaff, R. (2019) · IntechOpen eBooks · doi:10.5772/intechopen.86446 · Cited by 7
“CNN have very impressive and promising applications in image processing and pattern recognition [22, 43].”
Background
FILTERING CHAOS: A TECHNIQUE TO ESTIMATE DYNAMICAL AND OBSERVATIONAL NOISE IN NONLINEAR SYSTEMS
Orrell, D. (2005) · International Journal of Bifurcation and Chaos · doi:10.1142/s021812740501203x · Cited by 7
“As an example, Figure 3 demonstrates the technique for the Chua circuit (R. Madan, 1993; T. Matsumoto et al., 1985).”
Method
Synchronisation and Circuit Realisation of Chaotic Hartley System
Varan, M., Akgül, A., Güleryüz, E., et al. (2018) · Zeitschrift für Naturforschung A · doi:10.1515/zna-2018-0027 · Cited by 7
“Circuit realisation of chaotic signal becomes popular after Chua circuit first revealed the behaviour of chaos in a circuit [3].”
Background
Experimental mastering of nonlinear dynamics in circuits by sporadic pulses
Ruiz, P., Gutiérrez, J. M., & Güémez, J. (2006) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2006.06.095 · Cited by 7
“This versatility of nonlinear systems lies in the fact that chaotic motion includes an infinite number of embedded unstable periodic orbits, that can be stabilized or unstabilized by appropriate mechanisms.”
Background
ON THE ONSET OF QUASI-PERIODIC SOLUTIONS IN THIRD-ORDER NONLINEAR DYNAMICAL SYSTEMS
GENESIO, R., & GHILARDI, C. (2005) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127405014064 · Cited by 7
SPECTRAL AND CORRELATION ANALYSIS OF SPIRAL CHAOS
Анищенко, В. С., Вадивасова, Т. Е., Kopeikin, A. S., et al. (2003) · Fluctuation and Noise Letters · doi:10.1142/s0219477503001282 · Cited by 7
Synchronization-based scheme for calculating ambiguity functions of wideband chaotic signals
Hu, W. S., Liu, Z., & Li, C. (2008) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2008.4517011 · Cited by 7
Artificial life approach for continuous optimisation of non-stationary dynamical systems
Annunziato, M., Bruni, C., Lucchetti, M., et al. (2003) · Integrated Computer-Aided Engineering · doi:10.3233/ica-2003-10202 · Cited by 7
“The Chua’s circuit [5,8] has been considered for long time as a paradigm in studying the onset of chaotic phenomena.”
Experimental signal transmission by using synchronisedstate controlled cellular neural networks
Arena, P., Baglio, S., Fortuna, L., et al. (1996) · Electronics Letters · doi:10.1049/el:19960262 · Cited by 7
Autowaves and Spatio-Temporal Chaos in CNNs-Part 11: A Tutorial
Pivka, L. (1995) · Cited by 7
Bifurcation and Synchronization of Two Coupled Generators
Martynyuk, A. A., & Никитина, Н. В. (2017) · International Applied Mechanics · doi:10.1007/s10778-017-0806-6 · Cited by 6
Complicated behaviors and non-smooth bifurcation of a switching system with piecewise linearchaotic circuit
Li-Feng, W., Yong, G., & Yong, L. (2013) · Acta Physica Sinica · doi:10.7498/aps.62.110510 · Cited by 6
Efficient image transmission through analog error correction
Liu, Y., Li, J., & Xie, K. (2011) · IEEE International Workshop on Multimedia Signal Processing (MMSP) · doi:10.1109/mmsp.2011.6093827 · Cited by 6
“They are widely existent in the natural world and the engineering world (e.g. climate change, mechanical vibration, acoustic signals and ecology systems are all chaotic systems), and many of them can be realized or emulated using simple electric circuits (e.g. chua’s circuit [12]).”
Background
Target Speed Sensing Technique using Dilation Correlation of Ultrasonic Signal for Vehicle
Shin, S., & Choi, S. B. (2019) · IEEE Sensors Applications Symposium (SAS) · doi:10.1109/sas.2019.8706036 · Cited by 6
“At the transmitter, Chua’s circuit [9], the well-known and the simplest chaotic signal generator provides a chaotic signal.”
Background
When multilayer links exchange their roles in synchronization
Tang, L., Smith, K., Daley, K., & Belykh, I. V. (2022) · Physical review. E · doi:10.1103/physreve.106.024214 · Cited by 6
Chaotic Dynamics with Fuzzy Systems
Porto, D. (2006) · Springer eBooks · doi:10.1007/3-540-32502-6_2 · Cited by 6
Frequency-domain and time-domain methods for feedback nonlinear systems and applications to chaos control
Duan, Z., Wang, J., Yang, Y. Z., et al. (2007) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2007.08.034 · Cited by 6
“Many methods for chaos analysis and control have been established [28,46,47].”
BackgroundMethod
Chaos based key expansion function for block ciphers
Kazmi, S., & Ikram, N. (2011) · Multimedia Tools and Applications · doi:10.1007/s11042-011-0767-4 · Cited by 6
Nonlinear dynamics: Challenges and perspectives
Lakshmanan, M. (2005) · Pramana · doi:10.1007/bf02706208 · Cited by 6
Turing patterns in cellular neural networks
Chua, L. O., & Goraş, L. (1995) · International Journal of Electronics · doi:10.1080/00207219508926307 · Cited by 6
Experimental nonlinear physics
Lauterborn, W. H., Kurz, T., & Parlitz, U. (1997) · Journal of the Franklin Institute · doi:10.1016/s0016-0032(97)00028-8 · Cited by 6
Sampled-Data $\mathcal {L}_{2}-\mathcal {L}_{\infty }$ Consensus Control of Nonlinear Multi-Agent Systems
Fang, M., Li, X., Sang, C., & Jian-ping, Z. (2017) · IEEE Access · doi:10.1109/access.2017.2772834 · Cited by 6
“Example 2: Consider a multi-agent system of 10 agents where each agent is a Chua’s circuit [40]: ẋi1(t) = (−1− κ2)xi1(t)+ xi2(t)+ (κ1 − κ2)f (xi1(t)”
A novel technique for studying chaos using an electronic circuit based on op-amps
Shahid, U., Shafique, M. A., Iqbal, S., et al. (2017) · European Conference on Circuit Theory and Design · doi:10.1109/ecctd.2017.8093291 · Cited by 6
“Various nonlinear electronic circuits that exhibit chaotic behavior, have been described in the literature [12], [13], [14], [15], [16].”
Background
An IC diode for Chua's circuit
Cruz, J. M., & Chua, L. O. (1993) · International Journal of Circuit Theory and Applications · doi:10.1002/cta.4490210311 · Cited by 6
MODULAR ADAPTIVE CONTROL OF CHAOS IN CHUA'S CIRCUIT
Maganti, G. B., & Singh, S. N. (2005) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127405013812 · Cited by 6
Detecting Unstable Fixed Points Using Kalman Filters With Constraints
Walker, D. M., & SMALL, M. P. (2006) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/tcsi.2006.883859 · Cited by 6
“Illustrative examples using data from Chua's circuit [14], [15], and two other nonlinear dynamical systems are studied to demonstrate the potential of the method in Section IV.”
Method
Digital communication systems, using chaos
Старков, С. О., & Yemetz, S. V. (2002) · International Conference on Control of Oscillations and Chaos (COC) · doi:10.1109/coc.1997.631327 · Cited by 6
Control of Chaotic Systems
Ushio, T. (1995) · Journal of Japan Society for Fuzzy Theory and Intelligent Informatics · doi:10.3156/jfuzzy.7.3_475 · Cited by 6
Localization Method of Compact Invariant Sets with Application to the Chua System
Gribov, A. F., Kanatnikov, A. N., & Крищенко, А. П. (2016) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127416500735 · Cited by 5
“(2) Both systems have a complex dynamical behavior which is analyzed in many publications, see [Belykh & Chua, 1992, 1993; Madan, 1993; Duan et al., 2007; Bilotta & Pantano, 2008; Algaba & Merino, 2011; Leonov & Kuznetsov, 2013; MedranoT & Rocha, 2014] and references therein.”
Background
Optimal placement of sensor and actuator for controlling the piecewise linear Chua circuit via a discretized controller
Letellier, C., Minati, L., & Barbot, J. (2023) · The Journal of Difference Equations and Applications · doi:10.1080/10236198.2022.2161899 · Cited by 5
“The Chua circuit is, by virtue of its minimal complexity and remarkable potential to generate diverse dynamics, is commonly taken as paradigmatic for chaos in many natural and artificial systems, such as electronic oscillators [27,60].”
Background
Two-cell cellular neural networks: generation of new hyperchaotic multiscroll attractors
Cafagna, D., & Grassi, G. (2004) · doi:10.1109/ijcnn.2003.1223814 · Cited by 5
Hopping probabilities in a chaotic attractor
Etchegoin, P. (2001) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(01)00376-4 · Cited by 5

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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