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Spatiotemporal parametric instabilities in a soft strip

E. Duval1,2,3, F. Pétrélis2,3, V. Tournat1, J. Asnacios2, S. Fauve3, and M. Lanoy1,2

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Phys. Rev. E 114, L022201 – Published 7 August, 2026

DOI: https://doi.org/10.1103/qdqp-d295

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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Information

Phys. Rev. E 114, L022201– Published 7 August, 2026
  • Received 8 July 2025
  • Accepted 13 July 2026
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