Experimental characterization of nonlinear systems: a real-time evaluation of the analogous Chua’s circuit behavior

Rocha, Ronilson; Andrucioli, Guilherme Lúcio Damião; Medrano-T, Rene O.

doi:10.1007/s11071-010-9714-6

Cited by 17 publications

(7 citation statements)

References 11 publications

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“…In this work, we have studied a forced chaotic system that is a modified version of the Chua's circuit [8][9][10][11][12] with a very simple forcing mechanism, i.e., a series dc voltage source with the Chua's diode (see Fig. 1(a)) [12].…”

Section: Introductionmentioning

confidence: 99%

Periodicity detection on the parameter-space of a forced Chua’s circuit

et al. 2011

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We report a Periodicity-Detection algorithm, implemented in a LabVIEW routine for realtime data analysis on experimental chaos, to evaluate the periodicity P of experimental time series. The Periodicity-Detector (PD) algorithm was applied to the forced Chua's circuit with the aim to build the Periodicity-parameter-space (P -parameter-space). As results of the P -parameter-space, we could observe very complex dynamical behaviors, as regions of periodic structures, a new sequence of accumulation boundary, and the periodic structures organizing themselves in a period-adding bifurcation cascade. Those results agree with the maximal Lyapunov exponent and the bifurcation diagram analysis, presented in a previous work.

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Section: Introductionmentioning

confidence: 99%

Periodicity detection on the parameter-space of a forced Chua’s circuit

et al. 2011

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“…The following aspects of the time series are analyzed in order to perform the experimental characterization of the dynamic behavior of the system: time waveforms, phase portraits, frequency spectra, Poincaré sections, and bifurcation diagram. The real-time analysis of the acquired data are performed using LabVIEW codes described in [Rocha et al, 2010].…”

Section: Resultsmentioning

confidence: 99%

“…In this system, domains of periodicity immersed in chaotic regions of 2D parameter space are organized in period-adding cascades with spiral configurations along homoclinic bifurcations [Komuro et al, 1991;Albuquerque & Rech, 2012]. Moreover, the implementation of Chua's circuit is easy and allows to perform experiments whose results present great agreement with computational simulations [Matsumoto et al, 1985;Zhong & Ayrom, 1985;Weldon, 1990;Cruz & Chua, 1992;Kennedy, 1992;Cruz & Chua, 1993;Rodriguez-Vazquez & Delgado-Restituto, 1993;Morgül, 1995;Senani & Gupta, 1998;Elwakil & Kennedy, 2000;Tôrres & Aguirre, R. O. Medrano-T & R. Rocha 2000;Kiliç et al, 2002;Barboza, 2008;Rocha & Medrano-T, 2009;Trejo-Guerra et al, 2010;Rocha et al, 2010;Banerjee, 2012].…”

Section: Introductionmentioning

confidence: 92%

The Negative Side of Chua's Circuit Parameter Space: Stability Analysis, Period-Adding, Basin of Attraction Metamorphoses, and Experimental Investigation

Medrano-T

Rocha

2014

Int. J. Bifurcation Chaos

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Although Chua's circuit is one of the most studied nonlinear dynamical systems, its version with negative parameters remains practically untouched. This work reports an interesting and rich dynamic scenery that was hidden in this almost unexplored region. The study is focused on 2D parameter space and presents an analysis of stability based on describing functions. Numerical investigations present a gallery of period-adding cascades and a strong presence of basin boundary metamorphoses. The key to this new scenario is that for negative parameters, Chua's system does not satisfy the Shilnikov condition and it is shown that the homoclinic orbit organizes the parameter space completely different from as known. The obtained experimental results corroborate with the numerical and theoretical investigations.

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“…Chua's map, [15], [17] ,is related to Chua's electric circuit theory that exhibits classic chaos theory behavior invented by Japanese Prof. Leon O. Chua in 1983. This means roughly that it is a "nonperiodic oscillator"; it produces an oscillating waveform that, unlike an ordinary electronic oscillator, never • N R is a nonlinear negative resistance called a Chua's diode.…”

Section: Chua's Circuitmentioning

confidence: 99%

Complexity Studies in Some Piecewise Continuous Dynamical Systems

Chitkara

Kumra

Saha

2016

MJIS

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The, "Complex systems", stands as a broad term for many diverse disciplines of science and engineering including natural & medical sciences. Complexities appearing in various dynamical systems during evolution are now interesting subjects of studies. Chaos appearing in various dynamical systems can also be viewed as a form of complexity. For some cases nonlinearities within the systems and for other cases piecewise continuity property of the system are responsible for such complexity. Dynamical systems represented by mathematical models having piecewise continuous properties show strange complexity character during evolution. Interesting recent articles explain widely on complexities in various systems. Observable quantities for complexity are measurement of Lyapunov exponents (LCEs), topological entropies, correlation dimension etc.The present article is related to study of complexity in systems having piecewise continuous properties. Some mathematical models are considered here in this regard including famous Lozi map, a discrete mathematical model and Chua circuit, a continuous model. Investigations have been carried forward to obtain various attractors of these maps appearing during evolution in diverse and interesting pattern for different set of values of parameters and for different initial conditions. Numerical investigations extended to obtain bifurcation diagrams, calculations of LCEs, topological entropies and correlation dimension together with their graphical representation.

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Experimental characterization of nonlinear systems: a real-time evaluation of the analogous Chua’s circuit behavior

Cited by 17 publications

References 11 publications

Periodicity detection on the parameter-space of a forced Chua’s circuit

Periodicity detection on the parameter-space of a forced Chua’s circuit

The Negative Side of Chua's Circuit Parameter Space: Stability Analysis, Period-Adding, Basin of Attraction Metamorphoses, and Experimental Investigation

Complexity Studies in Some Piecewise Continuous Dynamical Systems

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