Parameter space of experimental chaotic circuits with high-precision control parameters

Francisco F. G. de Sousa, Rero M. Rubinger, Jose C. Sartorelli, Holokx A. Albuquerque, Murilo S. Baptista

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Abstract

We report high-resolution measurements that experimentally confirm a spiral cascade structure and a scaling relationship of shrimps in the Chua's circuit. Circuits constructed using this component allow for a comprehensive characterization of the circuit behaviors through high resolution parameter spaces. To illustrate the power of our technological development for the creation and the study of chaotic circuits, we constructed a Chua circuit and study its high resolution parameter space. The reliability and stability of the designed component allowed us to obtain data for long periods of time (∼21 weeks), a data set from which an accurate estimation of Lyapunov exponents for the circuit characterization was possible. Moreover, this data, rigorously characterized by the Lyapunov exponents, allows us to reassure experimentally that the shrimps, stable islands embedded in a domain of chaos in the parameter spaces, can be observed in the laboratory. Finally, we confirm that their sizes decay exponentially with the period of the attractor, a result expected to be found in maps of the quadratic family.
Electronic circuits provide a simple alternative to test in the laboratory theoretical approaches developed to characterize more complex systems. So far, however, experiments were being carried out in circuits with course-grained parameter values. In this work, we present a novel electronic architecture for a potentiometer that permits fine variations in control parameters. To demonstrate the usefulness of this potentiometer to the behavioral analysis of electronic circuits, we make very long time-series measurements of this circuit for a fine variation of its parameters and experimentally report, for the first time, that stable islands embedded in a domain of chaos in the parameter spaces indeed have sizes that decay exponentially with the period of the attractor. Periodicity with high period, confirmed by the calculation of the Lyapunov exponents, thus requires fine tuning of parameters to be experimentally observed.
Original languageEnglish
Article number083107
Pages (from-to)1-7
Number of pages7
JournalChaos
Volume26
Issue number8
Early online date8 Aug 2016
DOIs
Publication statusPublished - Aug 2016

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Chaotic Circuit
Control Parameter
Parameter Space
Networks (circuits)
Lyapunov Exponent
Chua's Circuit
High Resolution
Electronics
Attractor
Chaos
exponents
Decay
Chaos theory
chaos
high resolution
electronics
Period of time
Periodicity
Cascade
Complex Systems

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de Sousa, F. F. G., Rubinger, R. M., Sartorelli, J. C., Albuquerque, H. A., & Baptista, M. S. (2016). Parameter space of experimental chaotic circuits with high-precision control parameters. Chaos, 26(8), 1-7. [083107 ]. https://doi.org/10.1063/1.4960582

Parameter space of experimental chaotic circuits with high-precision control parameters. / de Sousa, Francisco F. G. ; Rubinger, Rero M.; Sartorelli, Jose C. ; Albuquerque, Holokx A. ; Baptista, Murilo S.

In: Chaos, Vol. 26, No. 8, 083107 , 08.2016, p. 1-7.

Research output: Contribution to journalArticle

de Sousa, FFG, Rubinger, RM, Sartorelli, JC, Albuquerque, HA & Baptista, MS 2016, 'Parameter space of experimental chaotic circuits with high-precision control parameters', Chaos, vol. 26, no. 8, 083107 , pp. 1-7. https://doi.org/10.1063/1.4960582
de Sousa, Francisco F. G. ; Rubinger, Rero M. ; Sartorelli, Jose C. ; Albuquerque, Holokx A. ; Baptista, Murilo S. / Parameter space of experimental chaotic circuits with high-precision control parameters. In: Chaos. 2016 ; Vol. 26, No. 8. pp. 1-7.
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AU - Baptista, Murilo S.

N1 - ACKNOWLEDGMENTS The authors thank Professor Iberê Luiz Caldas for the suggestions and encouragement. The authors F.F.G.d.S., R.M.R., J.C.S., and H.A.A. acknowledge the Brazilian agency CNPq and state agencies FAPEMIG, FAPESP, and FAPESC, and M.S.B. also acknowledges the EPSRC Grant Ref. No. EP/I032606/1.

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N2 - We report high-resolution measurements that experimentally confirm a spiral cascade structure and a scaling relationship of shrimps in the Chua's circuit. Circuits constructed using this component allow for a comprehensive characterization of the circuit behaviors through high resolution parameter spaces. To illustrate the power of our technological development for the creation and the study of chaotic circuits, we constructed a Chua circuit and study its high resolution parameter space. The reliability and stability of the designed component allowed us to obtain data for long periods of time (∼21 weeks), a data set from which an accurate estimation of Lyapunov exponents for the circuit characterization was possible. Moreover, this data, rigorously characterized by the Lyapunov exponents, allows us to reassure experimentally that the shrimps, stable islands embedded in a domain of chaos in the parameter spaces, can be observed in the laboratory. Finally, we confirm that their sizes decay exponentially with the period of the attractor, a result expected to be found in maps of the quadratic family.Electronic circuits provide a simple alternative to test in the laboratory theoretical approaches developed to characterize more complex systems. So far, however, experiments were being carried out in circuits with course-grained parameter values. In this work, we present a novel electronic architecture for a potentiometer that permits fine variations in control parameters. To demonstrate the usefulness of this potentiometer to the behavioral analysis of electronic circuits, we make very long time-series measurements of this circuit for a fine variation of its parameters and experimentally report, for the first time, that stable islands embedded in a domain of chaos in the parameter spaces indeed have sizes that decay exponentially with the period of the attractor. Periodicity with high period, confirmed by the calculation of the Lyapunov exponents, thus requires fine tuning of parameters to be experimentally observed.

AB - We report high-resolution measurements that experimentally confirm a spiral cascade structure and a scaling relationship of shrimps in the Chua's circuit. Circuits constructed using this component allow for a comprehensive characterization of the circuit behaviors through high resolution parameter spaces. To illustrate the power of our technological development for the creation and the study of chaotic circuits, we constructed a Chua circuit and study its high resolution parameter space. The reliability and stability of the designed component allowed us to obtain data for long periods of time (∼21 weeks), a data set from which an accurate estimation of Lyapunov exponents for the circuit characterization was possible. Moreover, this data, rigorously characterized by the Lyapunov exponents, allows us to reassure experimentally that the shrimps, stable islands embedded in a domain of chaos in the parameter spaces, can be observed in the laboratory. Finally, we confirm that their sizes decay exponentially with the period of the attractor, a result expected to be found in maps of the quadratic family.Electronic circuits provide a simple alternative to test in the laboratory theoretical approaches developed to characterize more complex systems. So far, however, experiments were being carried out in circuits with course-grained parameter values. In this work, we present a novel electronic architecture for a potentiometer that permits fine variations in control parameters. To demonstrate the usefulness of this potentiometer to the behavioral analysis of electronic circuits, we make very long time-series measurements of this circuit for a fine variation of its parameters and experimentally report, for the first time, that stable islands embedded in a domain of chaos in the parameter spaces indeed have sizes that decay exponentially with the period of the attractor. Periodicity with high period, confirmed by the calculation of the Lyapunov exponents, thus requires fine tuning of parameters to be experimentally observed.

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