Chua Circuit Bibliography

Chua Circuit Bibliography 

(working links as of 12/18/2019)

I'm continuing with oscillating circuit experiments. More inductors are being delivered in the next few weeks. This is a list of Chua Diode and Circuit articles with working (free) links. Some are pretty advanced and focus on equations and synchronization--the earlier the year of publication the more physical circuit-based (fun) it will be if you're building your own circuits and playing with oscilloscopes or LTspice:

·          Aguirre, L.A. [1995] "The use of identified models in the control of a chaotic circuit," 1995 IEEE International Symposium on Circuits and Systems (Cat. No.95CH35771). IEEE. Part vol.2, pp.1528-1531.

·          Aguirre, L.A., Souza, A.V.P. [1998] "An algorithm for estimating fixed points of dynamical systems from time series," International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, vol.8, no.11, pp.2203-2213.

·          Aguirre, L.A., Torres, L.A.B. [1997] "Fixed point stability analysis of Chua's circuit: a case study with a real circuit," Journal of Circuits Systems & Computers, vol.7, no.2, pp.111-115.

·          Aissi, C., Fadul, F. [1997] "Chaos in conditionally reset linear systems," Journal of Circuits Systems & Computers, vol.7, no.3, pp.177-189.

·          Alexeyev, A.A., Osipov, G.V., Shalfeev, V.D. [1995] "Effects of square-wave modulation on CNN patterns," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.42, no.10, pp.700-705.

·          Algaba, A., Freire, E., Gamero, E., Rodriguez-Luis, A.J. [1999] "On the Takens-Bogdanov bifurcation in the Chua's equation," IEICE Transactions on Fundamentals of Electronics Communications & Computer Sciences, vol.E82-A, no.9, pp.1722-1728.

·          Altman, E.J. [1993] "Normal Form Analysis of Chua`s Circuit with Applications for Trajectory Recognition," IEEE Transactions on Circuits & Systems II-Analog & Digital Signal Processing, vol.40, no.10, pp.675-682.

·          Alvarez, J., Alvarez, J., Velasco, M. [1997] "Approximate model-matching for nonlinear systems with a small time-delay; application to a chaotic Chua circuit," Proceedings of the 36th IEEE Conference on Decision and Control (Cat. No.97CH36124). IEEE. Part vol.2, pp.1631-1636.

·          Anishchenko, V.S., Kapitaniak, T., Safonova, M.A., Sosnovzeva, O.V. [1994] "Birth of double-double scroll attractor in coupled Chua circuits," Physics Letters A, vol.192, no.2-4, pp.207-214.

·          Anshan, H. [1988] "A Study of the Chaotic Phenomena in Chua's Circuit," Proceedings of 1988 IEEE International Symposium on Circuits and Systems (Cat. No.88CH2458-8). IEEE. vol.1, pp.273-276.

·          Arena, P., Baglio, S., Fortuna, L., Manganaro, G. [1995] "Chua's circuit can be generated by CNN cells," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.42, no.2, pp.123-125.

·          Arena, P., Baglio, S., Fortuna, L., Manganaro, G. [1995] "Simplified scheme for realisation of Chua oscillator by using SC-CNN cells," Electronics Letters, vol.31, no.21, pp.1794-1795.

·          Arena, P., Baglio, S., Fortuna, L., Xibilia, M.G. [1995] "Chaotic time series prediction via quaternionic multilayer perceptrons," 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century (Cat. No.95CH3576-7). IEEE. Part vol.2, pp.1790-1794.

·          Arena, P., Caponetto, R., Fortuna, L., Muscato, G., Xibilia, M.G. [1996] "Quaternionic multilayer perceptrons for chaotic time series prediction," IEICE Transactions on Fundamentals of Electronics Communications & Computer Sciences, vol.E79-A, no.10, pp.1682-1688.

·          Arena, P., Fortuna, L., Porto, D., Rizzo, A. [1999] "Self-organisation in arrays of nonlinear systems induced by chaotic perturbation: An experimental approach," ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349). IEEE. Part vol.5, pp.479-482.

·          Astakhov, V., Shabunin, A., Anishchenko, V. [1998] "Synchronization of self-oscillations by parametric excitation," International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, vol.8, no.7, pp.1605-1612.

·          Bartissol, P., Chua, L.O. [1988] "The Double Hook (Nonlinear Chaotic Circuits)," IEEE Transactions on Circuits & Systems, vol.35, no.12, pp.1512-1522.

·          Bernardo, M.Di [1996] "A purely adaptive controller to synchronize and control chaotic systems," Physics Letters A, vol.214, no.3-4, 13 May 1996, pp.139-144.

·          Berns, D.W., Moiola, J.L., Guanrong, C. [1998] "Predicting period-doubling bifurcations and multiple oscillations in nonlinear time-delayed feedback systems," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.45, no.7, pp.759-763.

·          Berns, D.W., Moiola, J.L., Guanrong, C. [1998] "Predicting period-doubling bifurcations in nonlinear time-delayed feedback systems," Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187). IEEE. Part vol.3, pp.619-622.

·          Biey, M., Bonani, F., Gilli, M., Maio, I. [1996] "Influence of the parasitics on the time delayed Chua's circuit," 8th Mediterranean Electrotechnical Conference. Industrial Applications in Power Systems, Computer Science and Telecommunications. Proceedings (Cat. No.96CH35884). IEEE. Part vol.1, pp.443-446.

·          Biey, M., Bonani, F., Gilli, M., Maio, I. [1997] "Qualitative Analysis of the Dynamics of the Time-delayed Chua's Circuit," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.44, no.6, pp.486-500.

·          Biey, M., Gilli, M., Maio, I., Premoli, A. [1998] "A computer program for accurate time-domain analysis of 1D-arrays of Chua's oscillators," Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187). IEEE. Part vol.3, pp.383-386.

·          Bonani, F., Gilli, M. [1999] "A harmonic balance approach to bifurcation analysis of limit cycles," ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349). IEEE. Part vol.6, pp.298-301.

·          Bonani, F., Gilli, M. [1999] "Analysis of stability and bifurcations of limit cycles in Chua's circuit through the harmonic-balance approach," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.46, no.8, pp.881-890.

·          Bonet, J., Pala, P., Milo, J.M. [1998] "A discrete-time approach to the steady state analysis of distributed nonlinear autonomous circuits," Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187). IEEE. Part vol.3, pp.460-464.

·          Bonet-Dalmau, J., Pala-Schonwalder, P., del Aguila-Lopez, F. [1999] "Steady state analysis of Chua's circuit with RLCG transmission line," ICECS'99. Proceedings of ICECS '99. 6th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.99EX357). IEEE. Part vol.2, pp.819-822.

·          Broucke, M.E. [1987] "One Parameter Bifurcation Diagram for Chua's Circuit," IEEE Transactions on Circuits & Systems, vol.CAS-34, no.2, pp.208-209.

·          Brown, R. [1993] "Generalizations of the Chua Equations," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.40, no.11, pp.878-884.

·          Brucoli, M., Cafagna, D., Carnimeo, L., Grassi, G. [1996] "Hyperchaotic circuits for secure communications: an efficient synchronization technique," Proceedings of the Third IEEE International Conference on Electronics, Circuits, and Systems. ICECS '96 (Cat. No.96TH8229). IEEE. Part vol.2, pp.639-642.

·          Brucoli, M., Cafagna, D., Carnimeo, L., Grassi, G. [1998] "Synchronization of hyperchaotic circuits via continuous feedback control with application to secure communications," International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, vol.8, no.10, pp.2031-2040.

·          Brucoli, M., Cafagna, D., Carnimeo, L., Grassi, G. [1999] "Design of a hyperchaotic cryptosystem: based on identical and generalized synchronization," International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, vol.9, no.10, pp.2027-2037.

·          Brucoli, M., Carnimeo, L., Grassi, G. [1996] "On the dynamics of hyperchaotic circuits: a new synchronization approach," 8th Mediterranean Electrotechnical Conference. Industrial Applications in Power Systems, Computer Science and Telecommunications. Proceedings (Cat. No.96CH35884). IEEE. Part vol.1, pp.435-438.

·          Bykov, V.V. [1998] "On bifurcations leading to chaos in Chua's circuit," International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, vol.8, no.4, pp.685-699.

·          Calvo, O., Cartwright, J.H.E. [1998] "Fuzzy control of chaos," World Scientific. International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, vol.8, no.8, pp.1743-1747.

·          Caponetto, R., Fortuna, L., Lavorgoa, M., Manganaro, G., Occhipinti, L.[1996] "Experimental study on chaotic synchronisation with non-ideal transmission channel," IEEE GLOBECOM 1996. Communications: The Key to Global Prosperity. Conference Record (Cat. No.96CH35942). IEEE. Part vol.3, pp.2083-2087.

·          Caponetto, R., Fortuna, L., Occhipinti, L., Xibilia, M.G. [1998] "Hyperchaotic dynamic generation via SC-CNNs for secure transmission applications," 1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227). IEEE. Part vol.1, pp.492-496.

·          Chen, G. [1997] "On Some Controllability Conditions for Chaotic Dynamics Control," Chaos Solitons & Fractals, vol.8, no.9, pp.1461-1470.

·          Chen, G., Dong, X. [1993] "Ordering Chaos of Chua's Circuit-A Feedback Control Approach," Proceedings of 1993 IEEE International Symposium on Circuits and Systems, vol.4, pp.2604-2607.

·          Choi, I. [1994] "Interactive exploration of a chaotic oscillator for generating musical signals in real-time concert performance," Journal of the Franklin Institute, vol.331B, no.6, pp.785-818.

·          Chua, L.O. [1992] "A Zoo of Strange Attractors from the Canonical Chua's Circuits," Proceedings of the 35th Midwest Symposium on Circuits and Systems (Cat. No.92CH3099-9). IEEE. vol.2, pp.916-926.

·          Chua, L.O. [1993] "Global Unfolding of Chua's Circuit," IEICE Transactions on Fundamentals of Electronics Communications & Computer Sciences, vol.E76-A, no.5, pp.704-734.

·          Chua, L.O. [1994] "Chua's circuit: ten years later," IEICE Transactions on Fundamentals of Electronics Communications & Computer Sciences, vol.E77-A, no.11, Nov. 1994, pp.1811-1822.

·          Chua, L.O. [1995] "A glimpse of nonlinear phenomena from Chua's oscillator," Philosophical Transactions of the Royal Society of London a Mathematical & Physical Sciences, vol.353, no.1701, pp.3-12.

·          Chua, L.O., Huynh, L.T. [1992] "Bifurcation Analysis of Chua's Circuit," Proceedings of the 35th Midwest Symposium on Circuits and Systems (Cat. No.92CH3099-9). IEEE. vol.1, pp.746-751.

·          Chua, L.O., Lin, G-N. [1990] "Canonical Realization of Chua's Circuit Family," IEEE Transactions on Circuits & Systems, vol.37, no.7, pp.885-902.

·          Chua, L.O., Lin, G-n. [1991] "Intermittency in a Piecewise-linear Circuit," IEEE Transactions on Circuits & Systems, vol.38, no.5, pp.510-20.

·          Chua, L.O., Pivka, L., Wu, C-W. [1995] "A universal circuit for studying chaotic phenomena," Philosophical Transactions of the Royal Society of London a Mathematical & Physical Sciences, vol.353, no.1701, pp.65-84.

·          Chua, L.O., Wu, C.W., Huang, A., Zhong, G-Q. [1993] "A Universal Circuit for Studying and Generating Chaos. I. Routes to Chaos," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.40, no.10, pp.732-744.

·          Chua, L.O., Wu, C.W., Huang, A., Zhong, G-Q. [1993] "A Universal Circuit for Studying and Generating Chaos. II. Strange Attractors," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.40, no.10, pp.745-761.

·          Chua, L.O., Yang, T., Zhong, G-Q., Wu, C-W. [1996] "Synchronization of Chua's circuits with time-varying channels and parameters," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.43, no.10, pp.862-868.

·          Chua, LO., Komuro, M., Matsumoto, T. [1986] "The Double Scroll Family," IEEE Transactions on Circuits & Systems, vol.CAS-33, no.11, pp.1073-1118.

·          Civalleri, P.P., Gilli, M. [1999] "Analysis of nonlinear dynamic arrays, through spatial mode decomposition," ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349). IEEE. Part vol.5, pp.310-313.

·          Claussen, J.C., Mausbach, T., Piel, A., Schuster, H.G. [1998] "Memory difference control of unknown unstable fixed points: Drifting parameter conditions and delayed measurement," Physical Review E. Statistical Physics, Plasmas, Fluids, & Related Interdisciplinary Topics, vol.58, no.6, pp.7256-7260.

·          Corron, N.J., Hahs, D.W. [1997] "A New Approach to Communications Using Chaotic Signals," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.44, no.5, pp.373-382.

·          Cruz, J.M., Chua, L.O. [1992] "A CMOS IC Nonlinear Resistor for Chua's Circuit," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.39, no.12, pp.985-995.

·          Cruz, J.M., Chua, L.O. [1993] "An IC Chip of Chua`s Circuit," IEEE Transactions on Circuits & Systems II-Analog & Digital Signal Processing, vol.40, no.10, pp.614-625.

·          Dabrowski, A.M., Dabrowski, W.R., Ogorzalek, M.J. [1993] "Dynamic Phenomena in Chain Interconnections of Chua's Circuits," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.40, no.11, pp.868-871.

·          Daqin, Z., Zhong, R., Shi, L., Shenchu, X. [1996] "Anti-jamming of chaotic signals," ICSP '96. 1996 3rd International Conference on Signal Processing Proceedings (Cat. No.96TH8116). IEEE. Part vol.1, pp.261-263.

·          Dedieu, H., Kennedy, M.P., Hasler, M. [1993] "Chaos Shift Keying: Modulation and Demodulation of a Chaotic Carrier Using Self-synchronizing Chua`s Circuits," IEEE Transactions on Circuits & Systems II-Analog & Digital Signal Processing, vol.40, no.10, pp.634-642.

·          Dedieu, H., Ogorzalek, M.J. [1997] "Identifiability and identification of chaotic systems based on adaptive synchronization," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.44, no.10, pp.948-962.

·          Delgado-Restituto, M., Linan, M., Rodriguez-Vazquez, A. [1996] "IC design for spread spectrum communication exploiting chaos," 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World, ISCAS 96 (Cat. No.96CH35876). IEEE. Part vol.3, pp.178-181.

·          Dellnitz, M., Field, M., Golubitsky, M., Hohmann, A., Jun, M. [1995] "Cycling chaos," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.42, no.10, pp.821-823.

·          Dellnitz, M., Junge, O. [1997] "Almost invariant sets in Chua's circuit," International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, vol.7, no.11, pp.2475-2485.

·          Doerner, R., Hubinger, B., Martienssen, W. [1994] "Advanced chaos forecasting," Physical Review E. Statistical Physics, Plasmas, Fluids, & Related Interdisciplinary Topics, vol.50, no.1, pp.R12-15.

·          Duchesne, L. [1993] "Using Characteristic Multiplier Loci to Predict Bifurcation Phenomena and Chaos - a Tutorial," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.40, no.10, pp.683-688.

·          Eguchi, K., Inoue, T., Tsuneda, A. [1999] "Synthesis and analysis of a digital chaos circuit generating multiple-scroll strange attractors," IEICE Transactions on Fundamentals of Electronics Communications & Computer Sciences, vol.E82-A, no.6, pp.965-972.

·          Elgar, S., Chandran, V. [1993] "Higher Order Spectral Analysis of Chua's Circuit," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.40, no.10, pp.689-692.

·          Elgar, S., Vanhoff, B., Aguirre, L.A., Freitas, U.S., Chandran, V. [1998] "Higher-order spectra of nonlinear polynomial models for Chua's circuit," International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, vol.8, no.12, pp.2425-2431.

·          Elwakil, A.S., Kennedy, M.P. [1999] "Chaotic oscillator configuration using a frequency dependent negative resistor," Journal of Circuits Systems & Computers, vol.9, no.3-4, pp.229-242.

·          Femat, R., Alvarez-Ramirez, J., Castillo-Toledo, B., Gonzalez, J. [1999] "On robust chaos suppression in a class of nondriven oscillators: application to the Chua's circuit," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.46, no.9, pp.1150-1152.

·          Fortuna, L., Manganaro, G., Muscato, G., Nunnari, G. [1996] "Parallel simulation of cellular neural networks," Computers & Electrical Engineering, vol.22, no.1, pp.61-84.

·          Fradkov, A.L., Markov, A. [1997] "Adaptive synchronization of chaotic systems based on speed gradient method and passification," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.44, no.10, pp.905-912.

·          Galias, Z. [1997] "Positive topological entropy of Chua's circuit: a computer assisted proof," International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, vol.7, no.2, pp.331-349.

·          Galias, Z., Ogorzalek, M.J. [1999] "Study of synchronized motions in a one-dimensional array of coupled chaotic circuits," International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, vol.9, no.11, pp.2219-2224.

·          Ge, S.S., Wang, C. [1999] "Adaptive control of uncertain Chua's circuits," Proceedings of the 1999 IEEE International Symposium on Intelligent Control Intelligent Systems and Semiotics (Cat. No.99CH37014). IEEE. pp.126-131.

·          Genesio, R., Tesi, A., Villoresi, F. [1993] "A Frequency Approach for Analyzing and Controlling Chaos in Nonlinear Circuits," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.40, no.11, pp.819-828.

·          Gilli, M. [1995] "A spectral approach for studying spatio-temporal chaos," 1995 IEEE International Symposium on Circuits and Systems (Cat. No.95CH35771). IEEE. Part vol.1, pp.251-254.

·          Gilli, M. [1995] "Investigation of chaos in large arrays of Chua's circuits via a spectral technique," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.42, no.10, pp.802-806.

·          Gilli, M., Maggio, G.M. [1996] "Predicting chaos through an harmonic balance technique: an application to the time-delayed Chua's circuit," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.43, no.10, pp.872-874.

·          Gomez-Gesteira, M., Decastro, M., Perez-Villar, V. [1999] "On the role of random transversal uncoupling on re-entry formation," International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, vol.9, no.11, pp.2231-2236.

·          Gomez-Gesteira, M., Perez-Munuzuri, V., Chua, L.O., Perez-Villar, V. [1995] "Coexistence of excitability, Hopf and Turing modes in a one-dimensional array of nonlinear circuits," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.42, no.10, pp.672-677.

·          Gomez-Gesteirfa, M., deCastro, M., Perez-Villar, V., Chua, L.O. [1999] "Experimental Chua's circuit arrays as an autowave simulator," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.46, no.4, pp.495-499.

·          Goras, L., Chua, L.O. [1995] "Turing patterns in CNNs. II. Equations and behaviors," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.42, no.10, pp.612-626.

·          Goras, L., Chua, L.O. [1996] "Turing patterns in CNN's based on a new cell," 1996 Fourth IEEE International Workshop on Cellular Neural Networks and their Applications Proceedings (CNNA-96) (Cat. No.96TH8180). IEEE. pp.103-108.

·          Goras, L., Chua, L.O., Leenaerts, D.M.W. [1995] "Turing patterns in CNNs. I. Once over lightly," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.42, no.10, pp.602-611.

·          Gotz, M., Feldmann, U., Schwarz, W. [1993] "Synthesis of Higher Dimensional Chua Circuits," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.40, no.11, pp.854-860.

·          Grassi, G., Mascolo, S. [1998] "Design of nonlinear observers for hyperchaos synchronization using a scalar signal," Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187). IEEE. Part vol.3, pp.283-286.

·          Grassi, G., Mascolo, S. [1998] "Synchronization of hyperchaotic cellular neural networks: a system theory approach," 1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227). IEEE. Part vol.2, pp.1504-1509.

·          Grassi, G., Mascolo, S. [1999] "Synchronizing high dimensional chaotic systems via eigenvalue placement with application to cellular neural networks," International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, vol.9, no.4, pp.705-711.

·          Guanrong, C. [1993] "Controlling Chua's Global Unfolding Circuit Family," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.40, no.11, pp.829-832.

·          Harada, Y., Masuda, K., Ogawa, A. [1996] "Dynamical behavior of acoustically coupled chaos oscillators," Fractals-An Interdisciplinary Journal on the Complex Geometry of Nature, vol.4, no.3, pp.407-414.

·          Hartley, T.T., Lorenzo, C.F., Killory Qammer, H. [1995] "Chaos in a fractional order Chua's system," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.42, no.8, pp.485-490.

·          Hartley, T.T., Mossayebi, F. [1995] "On the control of an array of Chua's systems," 1995 IEEE International Symposium on Circuits and Systems (Cat. No.95CH35771). IEEE. Part vol.2, pp.1536-1539.

·          Hein, S. [1993] "Exploiting Chaos to Suppress Spurious Tones in General Double-loop Sigma Delta Modulators," IEEE Transactions on Circuits & Systems II-Analog & Digital Signal Processing, vol.40, no.10, pp.651-659.

·          Hobson, P.R., Lansbury, A.N. [1996] "A simple electronic circuit to demonstrate bifurcation and chaos," Physics Education, vol.31, no.1, pp.39-43.

·          Hosny, E.A., Sobhy, M.I. [1994] "Analysis of chaotic behavior in lumped-distributed circuits applied to the time-delayed Chua's circuit," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.41, no.12, pp.915-918.

·          Hu, G., Jinghua, X., Chua, L.O., Pivka, L. [1998] "Controlling spiral waves in a model of two-dimensional arrays of Chua's circuits," Physical Review Letters, vol.80, no.9, pp.1884-1887.

·          Hu, G., Pivka, L, Zheleznyak, A.L. [1995] "Synchronization of a one-dimensional array of Chua's circuits by feedback control and noise," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.42, no.10, pp.736-740.

·          Huang, A. [1991] "Period Doubling and Period Plus One Law-chaotic Phenomena in Similar Chua's Circuit," China 1991 International Conference on Circuits and Systems. Conference Proceedings (Cat. No.91TH0387-1). IEEE. vol.2, pp.736-739.

·          Huang, A. [1996] "On bounds of the parametric range of bifurcation of Chua's circuit," IEEE Transactions on Circuits & Systems I-Fundamental Theory & Applications, vol.43, no.8, pp.691-695.

·          Huang, An., Yang T. [1997] "Comment on "A new feedback control of a modified Chua's circuit system," Physica D, vol.102, no.3-4, pp.364-366.

·          Hwang, C.C., Chow, H.Y., Wang, Y.K. [1996] "A new feedback control of a modified Chua's circuit system," Physica D, vol.92, no.1-2, pp.95-100.

·          Hwang, C-C., Hsieh, J-Y., Lin, R-S. [1997] "A linear continuous feedback control of Chua's circuit," Chaos Solitons & Fractals, vol.8, no.9, pp.1507-1515.

·          Itoh, M. [1999] "Experimental study of impulsive synchronization," ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349). IEEE. Part vol.5, pp.410-413.

·          Itoh, M., Murakami, H. [1995] "New communication systems via chaotic synchronizations and modulations," IEICE Transactions on Fundamentals of Electronics Communications & Computer Sciences, vol.E78-A, no.3, pp.285-290.

·          Itoh, M., Murakami, H., Chua, L.O. [1994] "Communication systems via chaotic modulations," IEICE Transactions on Fundamentals of Electronics Communications & Computer Sciences, vol.E77-A, no.6, pp.1000-1006.

·          Itoh, M., Murakami, H., Chua, L.O. [1994] "Controlling chaotic motions in Chua's circuit via tunnels," 1994 IEEE International Symposium on Circuits and Systems (Cat. No.94CH3435-5). IEEE. Part vol.6, pp.89-92.

·          Itoh, M., Murakami, H., Chua, L.O. [1994] "Performance of Yamakawa's chaotic chips and Chua's circuits for secure communications," 1994 IEEE International Symposium on Circuits and Systems (Cat. No.94CH3435-5). IEEE. Part vol.6, pp.105-108.

·          Itoh, M., Murakami, H., Chua, L.O. [1994] "Secure communication systems via Yamakawa's chaotic chips and Chua's circuits," Proceedings of the Third IEEE Conference on Fuzzy Systems. IEEE World Congress on Computational Intelligence (Cat. No.94CH3430-6). IEEE. Part vol.2, pp.1293-1296.

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Simplest Chaotic System with a Hyperbolic Sine

Simplest Chaotic System with a Hyperbolic Sine

Oscillating circuit using a TL084 op amp.
It's similar to Chua's Circuit with chaos, bifurcation, etc.

The two LEDs are there for use without an oscilloscope...here is a version by Sprott without LEDs: http://sprott.physics.wisc.edu/pubs/paper352.htm

I hate breadboards, oscillating circuits never seem to work, so here is my point-to-point wired beauty:

Ground clips from oscilloscope probes went to gathered ground wires from the op amp (which actually came off the positive output pins!). Clipped the probes onto the legs of a couple of the ceramic capacitors to take a reading.


Connected the two 9 volt batteries together and then ran positive wire and negative wire from the appropriate free battery posts.

Simple layout:

Good old TL084 pinout. I think I actually used TL084ACN (newer version):

Resistor R1 = 13kΩ,

All other resistors are 10kΩ.

All the capacitors are 0.01µF monolithic ceramic capacitors.

At first I kept getting the 'flying hotdog' which in the report of Liu, Sprott, Wang and Ma they accepted as a valid output. I was only getting it when nothing else was responding. Here is a pic of it, but it's not cool or interesting:






This is where the awesomeness starts! I had to touch my finger to the negative 9v battery output to get this circuit ring (actually it's a jerk circuit, so maybe it jerks?). This is because I didn't put a potentiometer at the double 9volt battery supply. It was full +/- 9 volts.



It is close to a chaotic attractor associated with a type I class 3 eigenvalue patttern.

This mimics (well, gets close anyway to) another valid response according to Liu et al's paper. It rarely showed up, because I wasn't varying the power supply much:

Chaos is a steady-state behavior possible in any nonlinear continuous system, if its order is above 2 in a forced circuit; or 3 in certain autonomous circuits.

 

We're just waiting for the thunder storm to pass by. 

BASIC vs SMALL BASIC 2020 Edition!!!

BASIC vs SMALL BASIC 2020 Edition!!!

So, here is an iterated logistic difference equation that I've posted about before showing animal population growth. I'm re-posting the old-timey BASIC version...and at the bottom giving the year 2019/2020 SMALL BASIC version that you can pop into Microsoft's still up and running (!) Small BASIC online app (there is a downloadable version too!).

First the original old-timey BASIC from 1980s version:

If you run it on an online BASIC simulator it works. For this, an online simulator works fine. Try this one:  https://repl.it/repls/InsignificantTepidEquipment


If you type "2" as your input the population hovers at around half an animal. If you type "5" as your starting population it goes to infinity (which is an error). So you need numbers less than 4 to keep it running true. The population levels out if you put in 1.5 as a start:


10 N=.1
20 INPUT"VALUE OF R";R
30 FOR I=1 TO 30
40 N1=R*N*(1-N)
50 PRINT N1
60 N=N1
70 NEXT I




Here is the screen capture of it in action:

Infinity: that's a lot of kitties! But an error in the program of going too high (R=5).

So here is R = 3.999

SMALL BASIC YEAR 2020 VERSION:

There is a new version of BASIC from Microsoft available as a download or an online simulator here: https://smallbasic-publicwebsite.azurewebsites.net/

It's called Small Basic...and the language is different!!! I had to use my mind-brain for about 2 minutes to port the program over (copy/paste, delete line numbers, search and find new variable command words like "textwindow.readnumber", etc.)


Here's a cut and paste version of the above script in the new language (it works, but doesn't give as many lines of results):

N=0.1

TextWindow.Write("What is the value of R? ")

R = TextWindow.ReadNumber()

FOR I=1 TO 30

N1=R*N*(1-N)

TextWindow.WriteLine("The result it " + N1 + ".")

N=N1

ENDfor

Each one of these lines is a seperate line in Small Basic (just number them 1, 2, 3, etc.) like this screenshot:

Oddly, it cannot handle decimals for the R value, so here is R=5:

Fun in (Small) BASIC for the year 2020!!!!!!!!!!!

How did I actually convert it? I pasted my old BASIC program into the new Microsoft Small Basic online window. It gave errors on almost every line.

Then I posted at the end a working program.

Then I compared them visually to see how they do know what they used to do and what new words (commands) did those things.  Old-timey "Print" became that "Textwindow.WriteLine" thing. Also, at the last line you must write "ENDfor" or else it won't run. Annoying but neat.

One day maybe I'll do the Fractal Mandelbrot program in the new Small Basic language.


Here's a cool modification that won't crash your computer since Small BASIC is modern:

N=0.1

TextWindow.Write("What is the value of R? ")

R = TextWindow.ReadNumber()

FOR I=1.00 TO 100.00

N1=R*N*(1-N)

TextWindow.WriteLine("The result it " + N1 + ".")

N=N1

ENDfor

See above, make the 4th line say "FOR I=1.00 to 100.00" and it will run a longer amount of lines.

You can make the second number 5000 and watch your computer just spew out the maths.

After a couple runs you need to copy and paste your program in again, it will stop working.

Of course, I wasn't saving and loading (or compiling) the program, just make changes. Copy,

click to reload the online simulator, re-paste in your program and make any changes. Annoying!

But fun.

-Happy Thanksgiving 2019!!!!