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On the destabilization of a periodically driven three-dimensional torus

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Abstract

We report experimental evidence of the destabilization of a 3D torus obtained when a small subharmonic perturbation is added to a 2D torus characteristic of a driven relaxation oscillator. The Poincaré sections indicate that the torus breakup is sensitive to the phase difference between the main driving frequency and its first subharmonic perturbing component. The observed transition confirms the Newhouse, Ruelle and Takens quasiperiodic transition to chaos on a 3D torus. Numerical results on a sinusoidally perturbed circle map mirror the experimental results and confirm the key role of the phase difference in the transition between distinct dynamical regimes.

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Authors and Affiliations

  1. Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, Largo E. Fermi 6, 50125, Florence, Italy

    S. Euzzor, F. T. Arecchi & R. Meucci

  2. Istituto di Biofisica, Consiglio Nazionale delle Ricerche, via G. Moruzzi 1, 56124, Pisa, Italy

    A. Di Garbo

  3. Aix Marseille University, Université de Toulon, CNRS, CPT, Marseille, France

    J.-M. Ginoux

  4. School of Medicine, Vita-Salute San Raffaele University, Milan, Italy

    S. Zambrano

  5. Division of Genetics and Cell Biology, IRCCS San Raffaele Scientific Institute, Milan, Italy

    S. Zambrano

  6. Department of Physics and Astronomy, Università di Firenze, Florence, Italy

    F. T. Arecchi & R. Meucci

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  1. S. Euzzor
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  2. A. Di Garbo
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  3. J.-M. Ginoux
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Correspondence to R. Meucci.

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Euzzor, S., Di Garbo, A., Ginoux, JM. et al. On the destabilization of a periodically driven three-dimensional torus. Nonlinear Dyn 103, 1969–1977 (2021). https://doi.org/10.1007/s11071-020-06174-5

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