Surface pressure data from the Viking Lander mission and from GCM simulations of the martian atmosphere have been analyzed using singular systems analysis. Very regular oscillations are found with frequencies that are distributed bimodally with peaks corresponding to periods of approximately 2-4 days and 5-7 days, respectively. Reconstructions of the amplitudes of the two oscillations are often negatively correlated; i.e., when the amplitude of one oscillation is large, that of the other is small. The GCM simulations show that the negative correlation in the amplitudes of the two oscillations can be explained as a flipping between two different wavenumber modes. In the absence of diurnal forcing in the model, transition from an unrealistically regular high frequency mode to a similarly unrealistic regular low frequency mode occurs at most once during the northern winter season. The diurnal cycle in the model, however, acts in a non-linear sense to stimulate the transitions between the two wavenumbers and thus increases the frequency of mode flipping events. The corresponding simulations bear a closer resemblance to the observations.