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

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Abstract

We report a Periodicity-Detection algorithm, implemented in a LabVIEW routine for real-time 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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Authors and Affiliations

  1. Departamento de Física, Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627, Pampulha, CEP 31270-901, Belo Horizonte, MG, Brazil

    E. R. Viana, F. O. Dias, A. G. de Oliveira & G. M. Ribeiro

  2. Departamento de Física e Química, Universidade Federal de Itajubá, Av. BPS, 1303, Pinheirinho, CEP 37500-903, Itajubá, MG, Brazil

    R. M. Rubinger

  3. Departamento de Física, Universidade do Estado de Santa Catarina, R. Paulo Malschitzki, Campus Universitário Prof. Avelino Marcante, Zona Industrial Norte, CEP 89219-710, Joinville, SC, Brazil

    H. A. Albuquerque

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  1. E. R. Viana
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  2. R. M. Rubinger
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  3. H. A. Albuquerque
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  4. F. O. Dias
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  5. A. G. de Oliveira
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  6. G. M. Ribeiro
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Correspondence to E. R. Viana.

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Viana, E.R., Rubinger, R.M., Albuquerque, H.A. et al. Periodicity detection on the parameter-space of a forced Chua’s circuit. Nonlinear Dyn 67, 385–392 (2012). https://doi.org/10.1007/s11071-011-9986-5

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  • DOI: https://doi.org/10.1007/s11071-011-9986-5

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