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 101–200 of 598

Secure communication using a chaos based signal encryption scheme
Murali, K., Yu, H., Varadan, V., & Leung, H. (2001) · IEEE Transactions on Consumer Electronics · doi:10.1109/30.982780 · Cited by 46
Learning of Chua's circuit attractors by locally recurrent neural networks
Cannas, B., Cincotti, S., Marchesi, M., et al. (2001) · Chaos Solitons & Fractals · doi:10.1016/s0960-0779(00)00174-0 · Cited by 47
Chua's diode and strange attractor: a three‐layer hardware–software co‐design for medical image confidentiality
Rajagopalan, S., Poori, S., Narasimhan, M., Sivaraman, R., Chandrasekar, V. K., Balasubramanian, R., Paramasivam, V. M., & Amirtharajan, R. (2020) · IET Image Processing · doi:10.1049/iet-ipr.2019.0562 · Cited by 46
“The Chua chaotic system was chosen in this work because of the following reasons [33]: 1.”
MethodInfluential
Interaction of chaotic rotating waves in coupled rings of chaotic cells
Mariño, I. P., Pérez-Muñuzuri, V., Pérez-Villar, V., Sánchez, E., & Matı́as, M. A. (1999) · Physica D Nonlinear Phenomena · doi:10.1016/s0167-2789(98)00303-0 · Cited by 45
Periodic Oscillations and Bifurcations in Cellular Nonlinear Networks
Gilli, M., Corinto, F., & Checco, P. (2004) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/tcsi.2004.827627 · Cited by 45
“The parameters and are defined in [20] and [26], whereas , , and represent the coupling coefficients and the ratio is assumed to be positive; denotes the well-known nonlinear memoryless resistance of Chua’s diode (see [20], [26]).”
BackgroundMethod
"No-CPU" Chaotic Robots: From Classroom to Commerce
Sooraska, P., & Klomkarn, K. (2010) · IEEE Circuits and Systems Magazine · doi:10.1109/mcas.2010.935740 · Cited by 44
“The dynamic equation of the circuit is described by [10]”
Method
Linear generalized synchronization of continuous-time chaotic systems
Lu, J., & Xi, Y. (2003) · Chaos Solitons & Fractals · doi:10.1016/s0960-0779(02)00471-x · Cited by 44
“…the following two dynamical systems _x ¼ f ðxÞ driving system _y ¼ gðy; hðxÞÞ response system ð1Þ where x 2 Rn is the state of the driving system, y 2 Rn is the state of response (driven) system, hðxÞ 2 Rm is the coupling between the driving and driven systems for driving the response system.”
Background
Nonlinear Sprott94 Case A chaotic equation: Synchronization and masking communication applications
Uyaroğlu, Y., & Pehli̇van, İ. (2010) · Computers & Electrical Engineering · doi:10.1016/j.compeleceng.2010.04.002 · Cited by 42
New results of study on generating multiple-scroll chaotic attractors
Yu, S. (2003) · Science in China Series F Information Sciences · doi:10.1360/03yf9009 · Cited by 42
A neural-network-based channel-equalization strategy for chaos-based communication systems
Feng, J., Tse, C. K., & Lau, F. C. M. (2003) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/tcsi.2003.813966 · Cited by 42
“The first system is based on the Hénon map [8] and the second one is the Chua’s system [9].”
Method
Nondegeneracy Conditions for Active Memristive Circuits
Riaza, R. (2010) · IEEE Transactions on Circuits & Systems II Express Briefs · doi:10.1109/tcsii.2010.2041816 · Cited by 41
“(A background on Chua’s circuit family can be found in [9] and [21]; recent results are discussed in [7], [13], [14], [20], and the references therein.”
Background
Chimera states in ensembles of bistable elements with regular and chaotic dynamics
Shepelev, I. A., Bukh, A. V., Strelkova, G. I., et al. (2017) · Nonlinear Dynamics · doi:10.1007/s11071-017-3805-6 · Cited by 41
Adding noise to improve measurement
Andò, B., & Graziani, S. (2001) · IEEE Instrumentation & Measurement Magazine · doi:10.1109/5289.911170 · Cited by 41
How similar is the performance of the cubic and the piecewise-linear circuits of Chua?
Ramírez-Ávila, G. M., & Gallas, J. A. C. (2010) · Physics Letters A · doi:10.1016/j.physleta.2010.10.046 · Cited by 39
“1, Chua’s circuit contains five linear elements (two capacitors, one inductor, and two resistors) and a nonlinear element, the so-called Chua’s diode ( NR), playing the role of a negative resistor, and which normally contains two additional parameters [1, 2, 3, 4, 5].”
Background
CHAOS DOES HELP MOTION CONTROL
Buscarino, A., Fortuna, L., Frasca, M., & Muscato, G. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127407019391 · Cited by 39
MASTER-SLAVE SYNCHRONIZATION OF GENERAL LUR'E SYSTEMS WITH TIME-VARYING DELAY AND PARAMETER UNCERTAINTY
Huang, H., Li, H., & Zhong, J. (2006) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127406014800 · Cited by 39
“Consider the following Chua’s Circuit [Madan, 1993] described by ẋ = a(y − h(x)) ẏ = x − y + z ż = −by (19) with nonlinear characteristic h(x) = m1x + 1/2(m0−m1)(|x+c|−|x−c”
Analysis of Hopf and Takens–Bogdanov Bifurcations in a Modified van der Pol–Duffing Oscillator
Algaba, A., Freire, E., Gamero, E., et al. (1998) · Nonlinear Dynamics · doi:10.1023/a:1008294110873 · Cited by 39
WINNING ENTRY OF THE K. U. LEUVEN TIME-SERIES PREDICTION COMPETITION
McNames, J., Suykens, J. A. K., & Vandewalle, J. P. L. (1999) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127499001048 · Cited by 39
“• q = 1: double scroll (2-scroll) [Chua et al., 1986; Chua, 1994; Madan, 1993]”
A Lorenz-type attractor in a piecewise-smooth system: Rigorous results
Белых, В. Н., Barabash, N. V., & Belykh, I. V. (2019) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.5115789 · Cited by 38
Limit Cycle and Boundary Equilibrium Bifurcations in Continuous Planar Piecewise Linear Systems
Ponce, E., Ros, J., & Vela, E. (2015) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127415300086 · Cited by 38
An Improved Chua's Circuit and Its Use in Hyperchaotic Circuit
Gandhi, G. (2005) · Analog Integrated Circuits and Signal Processing · doi:10.1007/s10470-005-0376-0 · Cited by 38
Ultrasonic Distance Measurement Method With Crosstalk Rejection at High Measurement Rate
Shin, S., Kim, M.-H., & Choi, S. B. (2018) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2018.2863999 · Cited by 38
“1) Chua’s Circuit: Chua’s circuit [32] is a well-known and the simplest autonomous electronic circuit that generates chaotic signals.”
Background
Robust H∞ synchronization of chaotic Lur’e systems
Huang, H., & Feng, G. (2008) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2959852 · Cited by 38
Digital redesign for controlling the chaotic Chua's circuit
Xu, J., Chen, G., & Shieh, L. S. (1996) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/7.543870 · Cited by 37
Experimental synchronization of single-transistor-based chaotic circuits
Fortuna, L., & Frasca, M. (2007) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2803882 · Cited by 36
Size instabilities in rings of chaotic synchronized systems
Matı́as, M. A., Güémez, J., Pérez-Muñuzuri, V., et al. (1997) · Europhysics Letters (EPL) · doi:10.1209/epl/i1997-00159-8 · Cited by 36
“The nonlinear characteristic of Chua’s circuit is defined in the form [13]”
Background
STUDY ON THE GLOBAL PROPERTY OF THE SMOOTH CHUA'S SYSTEM
Liao, X., Yu, P., Xie, S., et al. (2006) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127406016483 · Cited by 36
“…have extensively investigated chaos synchronization and its possible applications (e.g. see [Chua et al., 1993b, 1993c; Yang & Yang, 1993;Madan, 1993; Suykens & Vandewalle, 1994;Wu & Chua, 1994; Zhang, 1996; Curran & Chua, 1997; Guan et al., 2002; Chen & Lü, 2003; Jiang et al., 2000,…”
A NEW SYNCHRONIZATION PRINCIPLE FOR A CLASS OF LUR'E SYSTEMS WITH APPLICATIONS IN SECURE COMMUNICATION
Bowong, S., Kakmeni, F. M. M., & Koina, R. (2004) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127404010758 · Cited by 36
A polynomial approach for generating a monoparametric family of chaotic attractors via switched linear systems
Aguirre‐Hernández, B., Campos-Cantón, E., Lopez-Renteria, J. A., & Díaz-González, E.-C. (2015) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2014.12.012 · Cited by 33
“Since the work reported by [14] about n-Double scroll from the Chua’s system [15,16], there have been many different approaches to yield multi-scroll attractors in the last coupled decades.”
Background
Adaptive synchronization between chaotic dynamical systems of different order
Bowong, S., & McClintock, P. V. E. (2006) · Physics Letters A · doi:10.1016/j.physleta.2006.05.006 · Cited by 34
PARAMETER ESTIMATION USING KALMAN FILTERS WITH CONSTRAINTS
Walker, D. M. (2006) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127406015325 · Cited by 34
Experimental study of stochastic resonance in a Chua’s circuit operating in a chaotic regime
Korneta, W., Gomes, I., Mirasso, C. R., & Toral, R. (2006) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2006.05.016 · Cited by 34
Digital signal transmission with cascaded heterogeneous chaotic systems
Murali, K. (2000) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.63.016217 · Cited by 34
ON GLOBAL DYNAMIC BEHAVIOR OF WEAKLY CONNECTED OSCILLATORY NETWORKS
Gilli, M., Bonnin, M., & Corinto, F. (2005) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127405012661 · Cited by 34
DECOMPOSITION METHOD FOR STUDYING SMOOTH CHUA'S EQUATION WITH APPLICATION TO HYPERCHAOTIC MULTISCROLL ATTRACTORS
Cafagna, D., & Grassi, G. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127407017276 · Cited by 34
SHRIMP STRUCTURE AND ASSOCIATED DYNAMICS IN PARAMETRICALLY EXCITED OSCILLATORS
Zou, Y., Thiel, M., Romano, M. C., et al. (2006) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127406016987 · Cited by 34
“These programs have been applied to a variety of systems exhibiting complex dynamics that typically take place in scientific and engineering disciplines, such as 2D predatorprey models or a nonsmooth Chua’s circuit system [Madan, 1993].”
Background
A GALLERY OF CHUA ATTRACTORS: PART III
Bilotta, E., STRANGES, F., & Pantano, P. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127407017537 · Cited by 34
Input and output coupled nonlinear systems
Duan, Z., Wang, J., & Huang, L. (2005) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/tcsi.2004.842873 · Cited by 34
“According to the traditional [6]–[9] for Chua’s circuit, one knows that a canonical chaotic attractor exists in the first single Chua’s circuit in (27).”
Background
Wave propagation in ray-chaotic enclosures: paradigms, oddities and examples
Galdi, V., Pinto, I. M., & Felsen, L. B. (2005) · IEEE Antennas and Propagation Magazine · doi:10.1109/map.2005.1436220 · Cited by 33
Adaptive control and synchronization for a class of nonlinear chaotic systems using partial system states
Wang, Y., Wen, C., Soh, Y. C., et al. (2005) · Physics Letters A · doi:10.1016/j.physleta.2005.10.055 · Cited by 33
Synchronization in random networks with given expected degree sequences
Checco, P., Biey, M., & Kocarev, L. (2006) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2006.05.063 · Cited by 33
“In this table, the Chua’s circuit is used as an oscillator (see [31]) and all different forms of the connectivity matrix H are considered.”
The OPCL control method for entrainment, model-resonance, and migration actions on multiple-attractor systems
Jackson, E. A. (1997) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.166283 · Cited by 33
Robustness to noise in synchronization of complex networks
Buscarino, A., Gambuzza, L. V., Porfiri, M., et al. (2013) · Scientific Reports · doi:10.1038/srep02026 · Cited by 32
Chaotic behaviour of a fourth-order autonomous electric circuit
Koliopanos, C. L., Kyprianidis, I. M., Stouboulos, I. N., et al. (2002) · Chaos Solitons & Fractals · doi:10.1016/s0960-0779(02)00115-7 · Cited by 32
Exponential synchronization of chaotic Lur’e systems with delayed feedback control
Huang, H., Feng, G., & Cao, J. (2008) · Nonlinear Dynamics · doi:10.1007/s11071-008-9454-z · Cited by 32
A GALLERY OF CHUA ATTRACTORS: PART II
Bilotta, E., Pantano, P., & STRANGES, F. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127407017343 · Cited by 32
Chaotic time series prediction via quaternionic multilayer perceptrons
Arena, P., Baglio, S., Fortuna, L., et al. (2002) · Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and Cybernetics · doi:10.1109/icsmc.1995.538035 · Cited by 31
CHUA'S SINGULARITIES: GREAT MIRACLE IN CIRCUIT THEORY
Špány, V., Galajda, P., Guzan, M., et al. (2010) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127410027544 · Cited by 30
Normal form analysis of Chua's circuit with applications for trajectory recognition
Altman, E. J. (1993) · IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing · doi:10.1109/82.246170 · Cited by 30
Synchronization waves in arrays of driven chaotic systems
Lorenzo, M. N., Mariño, I. P., Pérez-Muñuzuri, V., et al. (1996) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.54.r3094 · Cited by 30
Synchronization of bidirectionally coupled chaotic Chen’s system with delay
Tarai, A., Poria, S., & Chatterjee, P. (2008) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2007.11.025 · Cited by 29
Chaos generator design with piecewise affine systems
Wu, T., Wang, L., & Yang, X. (2015) · Nonlinear Dynamics · doi:10.1007/s11071-015-2529-8 · Cited by 29
FIELD PROGRAMMABLE ANALOG ARRAY TO IMPLEMENT A PROGRAMMABLE CHUA'S CIRCUIT
Caponetto, R., Mauro, A. D., Fortuna, L., et al. (2005) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127405012806 · Cited by 29
Design considerations for integrated continuous-time chaotic oscillators
Delgado‐Restituto, M., & Rodriguez-Vazquez, A. (1998) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.669072 · Cited by 29
“synthesis of an IC-oriented Chua’s circuit [30].”
Homoclinic orbits in a piecewise linear Rössler-like circuit
Pisarchik, A. N., & Jaimes-Reátegui, R. (2005) · Journal of Physics Conference Series · doi:10.1088/1742-6596/23/1/014 · Cited by 29
“[3]), the interest to these systems has rose significantly in view of incredible potential applications of chaos theory to engineering study and in particular to secure communications [4].”
Background
A GALLERY OF CHUA ATTRACTORS: PART IV
Bilotta, E., Blasi, G. D., STRANGES, F., et al. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127407017665 · Cited by 29
“Chua Oscillator is the simplest third order nonlinear electronic circuit capable of producing a rich variety of chaotic behavior and is considered as a canonical system for the investigation of chaos [Chua et al., 1993a, 1993b; Madan, 1993; Bilotta et al., 2007a].”
BackgroundInfluential
Nonlinear systems synchronization for modeling two-phase microfluidics flows
Cairone, F., Anandan, P., & Bucolo, M. (2017) · Nonlinear Dynamics · doi:10.1007/s11071-017-3819-0 · Cited by 28
Separation and synchronization of piecewise linear chaotic systems
Arena, P., Buscarino, A., Fortuna, L., et al. (2006) · Physical Review E · doi:10.1103/physreve.74.026212 · Cited by 28
Limit cycles in planar continuous piecewise linear systems
Chen, H., Li, D., Xie, J., et al. (2016) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2016.12.006 · Cited by 28
On synchronization of three chaotic systems
Yan, J., & Li, C. (2004) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2004.06.055 · Cited by 28
STRANGE ATTRACTORS IN PERIODICALLY KICKED CHUA'S CIRCUIT
Wang, Q., & Oksasoglu, A. (2005) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127405012028 · Cited by 28
“The illustrative example we use in this paper is the well-known Chua’s circuit (or system) [Madan, 1993; Chua, 1994].”
Method
Homogeneous finite time observer for nonlinear systems with linearizable error dynamics
Perruquetti, W., & Floquet, T. (2007) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.2007.4434702 · Cited by 28
“The great simplicity and considerable robustness have made the Chua s circuit a paradigm to generate chaotic signals [ 28 ].”
Background
Autowaves and spatio-temporal chaos in CNNs. II. A tutorial
Pivka, L. (1995) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.473571 · Cited by 28
An inductor-free realization of the Chua’s circuit based on electronic analogy
Rocha, R., & Medrano-T, R. O. (2008) · Nonlinear Dynamics · doi:10.1007/s11071-008-9408-5 · Cited by 28
“In spite of its simplicity, this system presents a very rich dynamical behavior as: fixed point, Hopf, periodic, period doubling, homoclinic bifurcations, or chaotic attractors [5, 6].”
Background
Crisis-induced intermittency in a third-order electrical circuit
Kyprianidis, I. M., Petrani, M. L., Kalomiros, J. A., et al. (1995) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.52.2268 · Cited by 28
Generating Multi-Scroll Chaotic Attractors via Switched Fractional Systems
Sun, G., Wang, M., Huang, L., et al. (2011) · Circuits Systems and Signal Processing · doi:10.1007/s00034-011-9272-2 · Cited by 27
READING COMPLEXITY IN CHUA'S OSCILLATOR THROUGH MUSIC. PART I: A NEW WAY OF UNDERSTANDING CHAOS
Bilotta, E., GERVASI, S., & Pantano, P. (2005) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127405012156 · Cited by 27
“Many other papers aimed at confirming Chua’s circuit as a universal paradigm for studying chaos [Shil’nikov, 1993; Madan, 1992, 1993], as this is “the first real physical system where chaos is observed in laboratory, confirmed by computer simulation, proven mathematically by two independent…”
Background
Heterogeneous chaotic systems based cryptography
Murali, K. (2000) · Physics Letters A · doi:10.1016/s0375-9601(00)00420-5 · Cited by 27
RANK ONE CHAOS: THEORY AND APPLICATIONS
Wang, Q., & Oksasoglu, A. (2008) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127408021002 · Cited by 26
THE LANGUAGE OF CHAOS
Bilotta, E., & Pantano, P. (2006) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127406014988 · Cited by 26
The Negative Side of Chua's Circuit Parameter Space: Stability Analysis, Period-Adding, Basin of Attraction Metamorphoses, and Experimental Investigation
Medrano-T, R. O., & Rocha, R. (2014) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127414300250 · Cited by 26
“Chua’s system obeys this theorem for positive values of the control parameters, but on the negative side of the parameter space the Shilnikov condition fails [Madan, 1993].”
Background
Dynamic bifurcation and strange nonchaos in a two-frequency parametrically driven nonlinear oscillator
Durairaj, P., Kumarasamy, S., Palanivel, J., et al. (2017) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2017.02.020 · Cited by 26
At most two limit cycles in a piecewise linear differential system with three zones and asymmetry
Chen, H., & Tang, Y. (2018) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2018.08.004 · Cited by 26
Experiments on RF Band Communications Using Chaos
Dmitriev, A. S., Panas, A. I., Старков, С. О., et al. (1997) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127497001680 · Cited by 26
“The basic element of the chaotic module in the chaos generator obtained by decomposition of Chua’s circuit [Madan, 1993] into two subsystems (RLC and RCNR) [Figs.”
BackgroundMethodInfluential
Output synchronization of chaotic systems under nonvanishing perturbations
Lopez-Mancilla, D., & Cruz-Hernández, C. (2006) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2006.10.020 · Cited by 26
CHAOS-BASED SR FLIP–FLOP VIA CHUA'S CIRCUIT
Cafagna, D., & GRASSI, G. (2006) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127406015465 · Cited by 25
EXPERIMENTAL REALIZATION OF BINARY SIGNALS TRANSMISSION USING CHAOS
Cruz-Hernández, C., Lopez-Mancilla, D., Garcia-Gradilla, V., et al. (2005) · Journal of Circuits Systems and Computers · doi:10.1142/s0218126605002490 · Cited by 25
Parasitic Effects on Memristor Dynamics
Itoh, M., & Chua, L. O. (2016) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127416300147 · Cited by 24
A modified Rössler prototype-4 system based on Chua’s diode nonlinearity : Dynamics, multistability, multiscroll generation and FPGA implementation
Kuate, P. D. K., Tchendjeu, A. E. T., & Fotsin, H. B. (2020) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2020.110213 · Cited by 24
Observation of stochastic resonance for weak periodic magnetic field signal using a chaotic system
Silva, I. G., Korneta, W., Stavrinides, S. G., et al. (2020) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2020.105558 · Cited by 24
Emergent spiking in non-ideal memristor networks
Gale, E., Costello, B. D. L. D. L., & Adamatzky, A. (2012) · Microelectronics Journal · doi:10.1016/j.mejo.2014.06.008 · Cited by 22
FURTHER INVESTIGATION OF HYSTERESIS IN CHUA'S CIRCUIT
Borresen, J., & Lynch, S. (2002) · International Journal of Bifurcation and Chaos · doi:10.1142/s021812740200422x · Cited by 24
“Evidence for the existence of a small bistable region is shown and numerical methods are applied to determine the behavior of the solutions within this bistable region.”
BackgroundMethod
Learning in the Smart City: A Virtual and Augmented Museum Devoted to Chaos Theory
Bertacchini, F., Bilotta, E., Carini, M., et al. (2014) · Lecture notes in computer science · doi:10.1007/978-3-662-43454-3_27 · Cited by 24
Experimental chaos from non-autonomous electronic circuits
Lakshmanan, M., & Murali, K. (1995) · Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences · doi:10.1098/rsta.1995.0088 · Cited by 24
Torus-doubling bifurcations in four mutually coupled Chua's circuits
Zhong, G., Wu, C. W., & Chua, L. O. (1998) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.661689 · Cited by 24
Generation of broad-band chaos using blocking oscillator
Rulkov, N. F., & Volkovskii, A. (2001) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.928150 · Cited by 24
“Quite a few simple autonomous nonlinear circuits that posses chaotic dynamics have been proposed and studied, see for ex- ample [1]–[6].”
Background
Toward the Use of Chua's Circuit in Education, Art and Interdisciplinary Research: Some Implementation and Opportunities
Bertacchini, F., Bilotta, E., Gabriele, L., et al. (2013) · Leonardo · doi:10.1162/leon_a_00641 · Cited by 23
Experimental Stabilization of Unstable Periodic Orbit in Magneto-Elastic Chaos by Delayed Feedback Control
Hikihara, T., Touno, M., & Kawagoshi, T. (1997) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127497001916 · Cited by 23
“The OGY method exhibits effectiveness in many experimental examinations of different systems; for example, an electronic circuit [Madan, 1993], a laser system [Roy et al., 1992], a pendulum system [Hübinger et al., 1994] and so on.”
Method
CONTROL OF n-SCROLL CHUA'S CIRCUIT
Boukabou, A., SAYOUD, B., BOUMAIZA, H., et al. (2009) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127409025134 · Cited by 23
“Introduction Chua’s circuit is known as an electrical circuit and having the ability of generating chaos [Madan, 1993].”
Background
Analysis of nonlinear oscillatory network dynamics via time‐varying amplitude and phase variables
Lanza, V., Corinto, F., Gilli, M., et al. (2007) · International Journal of Circuit Theory and Applications · doi:10.1002/cta.433 · Cited by 23
“Finally, in Section 5 we consider, as case study, a network of four diffusively coupled third-order oscillators (Chua’s circuits [20, 21]) and we predict the bifurcations of limit cycles depending on the coupling parameters.”
Method
ONLINE SECURE CHATTING SYSTEM USING DISCRETE CHAOTIC MAP
Kwok, H. S., Tang, K. S., & Man, K. F. (2004) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127404009053 · Cited by 23
Diversity-induced coherence resonance in spatially extended chaotic systems
Chen, H., & Zhang, J. (2008) · Physical Review E · doi:10.1103/physreve.77.026207 · Cited by 23
A neural network associative memory for handwritten character recognition using multiple Chua characters
Baird, B., Hirsch, M. W., & Eeckman, F. H. (1993) · IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing · doi:10.1109/82.246169 · Cited by 23
“Here, we use the well-studied family of Chua attractors [ 6 ], [7] implemented by the Chua hardware circuit [8] to investigate the effectiveness of complex dynamics in this associative memory.”
Method
Is it really chaos? The complexity of transient dynamics of double pendula
Dudkowski, D., Wojewoda, J., Czołczyński, K., et al. (2020) · Nonlinear Dynamics · doi:10.1007/s11071-020-05697-1 · Cited by 22
Control of bifurcation-delay of slow passage effect by delayed self-feedback
Durairaj, P., Kumarasamy, S., Banerjee, T., et al. (2017) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4973237 · Cited by 22
A New 4D Chaotic System with Two‐Wing, Four‐Wing, and Coexisting Attractors and Its Circuit Simulation
Huang, L., Zhang, Z., Xiang, J., & Wang, S. (2019) · Complexity · doi:10.1155/2019/5803506 · Cited by 22
“Chua proposed Chua’s circuit in 1986 [10, 11], which was one of the simplest chaotic oscillation circuits.”
Background
Experimental pulse synchronisation of two chaotic circuits
Fortuna, L., Frasca, M., & Rizzo, A. (2003) · Chaos Solitons & Fractals · doi:10.1016/s0960-0779(02)00374-0 · Cited by 22
GENERATING 3-D SCROLL GRID ATTRACTORS OF FRACTIONAL DIFFERENTIAL SYSTEMS VIA STAIR FUNCTION
Deng, W. (2007) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127407019810 · Cited by 22
Experimental chaos from autonomous electronic circuits
Kennedy, M. P. (1995) · Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences · doi:10.1098/rsta.1995.0087 · Cited by 22
Homoclinic and heteroclinic orbits of the three-cell cellular neural networks
Zou, F., Katerle, A., & Nossek, J. A. (1993) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.251825 · Cited by 22

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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