Spatiotemporal parametric instabilities in a soft strip
Abstract
Period doubling is a robust feature of systems subjected to time-dependent parameter modulation, which manifests among a variety of fields including physics, chemistry, and biology. When the parameter is modulated in space, an analogous behavior can occur, characterized by the emergence of patterns with a wavelength twice that of the underlying modulation. Here, we consider the case of a system depending both on time and space. Using a simple mechanical model, here a vibrating strip, we show that such a modulation yields a dynamics richer than in the classical (i.e., purely temporal or spatial) case. In particular, instead of standard period doubling, we report a dual subharmonic response exhibiting occurrences of tristability. These features are captured within a unified framework, which further reveals that the frequency content of the response can be tuned via the ratio of the system size to the modulation length scale, a control parameter that can be adjusted through the strip's material properties, length, or tension.
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BibTeX
@article{duval2026spatiotemporal,
title = {{Spatiotemporal parametric instabilities in a soft strip}},
author = {E. Duval and F. Pétrélis and V. Tournat and J. Asnacios and S. Fauve and M. Lanoy},
journal = {Physical Review E},
year = {2026},
month = aug,
doi = {10.1103/qdqp-d295},
url = {https://hal.science/hal-05767750v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Spatiotemporal parametric instabilities in a soft strip
AU - E. Duval
AU - F. Pétrélis
AU - V. Tournat
AU - J. Asnacios
AU - S. Fauve
AU - M. Lanoy
PY - 2026
DA - 2026/08/07
JO - Physical Review E
DO - 10.1103/qdqp-d295
UR - https://hal.science/hal-05767750v1
AB - Period doubling is a robust feature of systems subjected to time-dependent parameter modulation, which manifests among a variety of fields including physics, chemistry, and biology. When the parameter is modulated in space, an analogous behavior can occur, characterized by the emergence of patterns with a wavelength twice that of the underlying modulation. Here, we consider the case of a system depending both on time and space. Using a simple mechanical model, here a vibrating strip, we show that such a modulation yields a dynamics richer than in the classical (i.e., purely temporal or spatial) case. In particular, instead of standard period doubling, we report a dual subharmonic response exhibiting occurrences of tristability. These features are captured within a unified framework, which further reveals that the frequency content of the response can be tuned via the ratio of the system size to the modulation length scale, a control parameter that can be adjusted through the strip's material properties, length, or tension.
SN - 2470-0045
SN - 2470-0053
ER -