We investigate time traces of the currents generated by the motion of electrons
on the surface of liquid helium that are placed in a perpendicular magnetic field
and exposed to microwave radiation. Nonlinear dynamics methods are utilized to
explore the characteristic features of the current oscillations from five electrodes
at different electron densities and pressing voltages. The wavelet phase coherence
and phase shift are calculated to obtain the coherence relationships between the
currents in the five electrodes, and the direction of motion of electrons inside the
cell, as functions of the pressing voltage. These classical methods reveal that the
electron motion is oscillatory with varying frequency and with a constant frequency modulation. Higher harmonics due to nonlinearity arise at higher frequencies where the the resonance condition for inter-subband transition is satisfied at a pressing voltage of 4.20 V for low electron density. Our approach provides a platform for investigating these phenomena analytically. We show that slow helium gravity waves modulate the electronic oscillatory behaviour and illustrate that the model in fact produces 3D dynamics. Motion of electrons on the surface of liquid helium is shown to be a paradigmatic example of a chronotaxic system, i.e. a system that undergoes continuous perturbation and is nonetheless capable of maintaining its stability.