  Oscillatory systems arise in the different science fields. Complex
mathematical formulations with differential equations have been proposed to
model the dynamics of these systems. While they have the advantage of having a
direct physiological meaning, they are not useful in practice as a result of
the parameter adjustment complexity and the presence of noise. In this paper, a
signal plus error model is proposed to analyze oscillations, where the signal
is a multicomponent $FMM$ and the noise is assumed Gaussian. The signal
formulation is also a novel decomposition approach in AM-FM components,
competing with Fourier and other decompositions. Several interesting
theoretical properties are derived including the Ordinary Differential
Equations describing the signal. Furthermore, the usefulness in real practice
is demonstrate to analyze signals associated to neuron synapses and by
addressing other questions in Neuroscience.
