Time reversal of the excitation wave form in a dissipative pattern-forming system

We discuss the consequences of time reversal of the excitation parameters on the stability of a periodically driven dynamic system. The example chosen, electrohydrodynamic convection of nematics, is a well-investigated dissipative pattern-forming system, usually driven with time-periodic external electric fields E(t) . The dynamic model that describes linear stability at onset can be represented by a set of two differential equations for the amplitudes of the dynamic variables. Floquet analysis reveals an astonishing dynamic property: Under time reversal of any periodic excitation function E(t) , the dynamic equations reproduce the same stability thresholds, pattern types, and critical pattern wavelengths, even when the dynamics of all involved system variables are essentially different for the excitations E(t) and E(-t) . Experimental confirmation of these mathematical predictions is provided by the measurement of threshold curves and the analysis of the time-resolved optical characteristics of the convection roll patterns.