# SIMPLE ELECTRONIC CHAOS GENERATORS AND THEIR CIRCUIT SIMULATION

Cite this article as:

Kuznetsov S. P. SIMPLE ELECTRONIC CHAOS GENERATORS AND THEIR CIRCUIT SIMULATION . Izvestiya VUZ, Applied Nonlinear Dynamics, 2018, vol. 26, iss. 3, pp. 35-61 DOI: 10.18500/0869-6632-2018-26-3-35-61

**Topic and aim.** The aim of the work is to review circuits of chaos generators, those described in the literature and some original ones, in a unified style basing on circuit simulations with the NI Multisim package, which makes the comparison of the various devices apparent. **Investigated models.** A number of electronic chaos generators are considered including the Kolpitz oscillator, the Hartley oscillator, the RC chaos generator, variants of Chua circuit, the designs proposed by the Lithuanian group, Lorenz analog oscillator, generators of hyperbolic chaos with excitation transfer between alternately excited oscillators, as well as a ring generator with delayed feedback. **Results.** The circuit diagrams of chaos generators are presented, the principles of their operation are discussed, and circuit simulations are carried out using the NI Multisim package. For all considered systems the chaotic dynamics are illustrated consistently by waveforms of the signals, phase portraits of the attractors, spectra of the oscillations. Specially outlined are generators of robust chaos including the electronic analog of the Lorenz model and the circuits with Smale–Williams hyperbolic attractors, which seem preferable for possible applications due to low sensitivity of the chaos characteristics to parameter variations, manufacturing imperfections, interferences, etc. **Discussion.** The circuits collected in the paper correspond to low-frequency devices, but some of them may be useful in development of chaos generators also at high and ultrahigh frequencies. The material presented may be of interest for setting up laboratory and computer practical courses aimed at training specialists in the field of electronics and nonlinear dynamics, as well as for researchers interested in constructing chaos generators and their practical applications.

DOI: 10.18500/0869-6632-2018-26-3-35-61

*References:* Kuznetsov S.P. Simple electronic chaos generators and their circuit simulation. Izvestiya VUZ, Applied Nonlinear Dynamics, 2018, vol. 26, no. 3, pp. 35–61. DOI: 10.18500/0869- 6632-2018-26-3-35-61

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## BibTeX

author = {Sergey P. Kuznetsov},

title = {SIMPLE ELECTRONIC CHAOS GENERATORS AND THEIR CIRCUIT SIMULATION },

year = {2018},

journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},

volume = {26},number = {3},

url = {http://andjournal.sgu.ru/en/articles/simple-electronic-chaos-generators-and-their-circuit-simulation},

address = {Саратов},

language = {russian},

doi = {10.18500/0869-6632-2018-26-3-35-61},pages = {35--61},issn = {0869-6632},

keywords = {dynamic system,chaos,Attractor,chaos generator,circuit simulation},

abstract = {Topic and aim. The aim of the work is to review circuits of chaos generators, those described in the literature and some original ones, in a unified style basing on circuit simulations with the NI Multisim package, which makes the comparison of the various devices apparent. Investigated models. A number of electronic chaos generators are considered including the Kolpitz oscillator, the Hartley oscillator, the RC chaos generator, variants of Chua circuit, the designs proposed by the Lithuanian group, Lorenz analog oscillator, generators of hyperbolic chaos with excitation transfer between alternately excited oscillators, as well as a ring generator with delayed feedback. Results. The circuit diagrams of chaos generators are presented, the principles of their operation are discussed, and circuit simulations are carried out using the NI Multisim package. For all considered systems the chaotic dynamics are illustrated consistently by waveforms of the signals, phase portraits of the attractors, spectra of the oscillations. Specially outlined are generators of robust chaos including the electronic analog of the Lorenz model and the circuits with Smale–Williams hyperbolic attractors, which seem preferable for possible applications due to low sensitivity of the chaos characteristics to parameter variations, manufacturing imperfections, interferences, etc. Discussion. The circuits collected in the paper correspond to low-frequency devices, but some of them may be useful in development of chaos generators also at high and ultrahigh frequencies. The material presented may be of interest for setting up laboratory and computer practical courses aimed at training specialists in the field of electronics and nonlinear dynamics, as well as for researchers interested in constructing chaos generators and their practical applications. DOI: 10.18500/0869-6632-2018-26-3-35-61 References: Kuznetsov S.P. Simple electronic chaos generators and their circuit simulation. Izvestiya VUZ, Applied Nonlinear Dynamics, 2018, vol. 26, no. 3, pp. 35–61. DOI: 10.18500/0869- 6632-2018-26-3-35-61 }}