#### Abstract

Do parametrically driven systems distinguish periodic excitations that are time mirrors of each other? Faraday waves in a Newtonian fluid are studied under excitation with superimposed harmonic wave forms. We demonstrate that the *threshold parameters* for the stability of the ground state are insensitive to a time inversion of the driving function. This is a peculiarity of some dynamic systems. The Faraday system shares this property with standard electroconvection in nematic liquid crystals [J. Heuer *et al.*, Phys. Rev. E **78**, 036218 (2008)]. In general, time inversion of the excitation affects the asymptotic stability of a parametrically driven system, even when it is described by linear ordinary differential equations. Obviously, the observed symmetry has to be attributed to the particular structure of the underlying differential equation system. The *pattern selection* of the Faraday waves above threshold, on the other hand, discriminates between time-mirrored excitation functions.

- Received 6 November 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.094503

© 2013 American Physical Society