In this paper we explore the radial motion of a spherical bubble oscillating immersed in a Newtonian fluid due to an harmonic acoustic pressure forcing. The ordinary differential Rayleigh-Plesset equation governs the non-linear motion of the bubble. Several non-linear responses of the bubble motion are explored and we discuss the in details how the main physical parameters, expressed in terms of the Reynolds and Weber numbers, influence the non-linear motion of this particular dynamic system. The methodology used to explore the problem is based on the control of the non-linear dynamic system. We also provide an asymptotic theory to predict how the buble radius vary with time for small amplitudes of the forcing presure field. Different vibrational modes of the bubble motion are examined for several values of the dynamical physical parameters Reynolds and Weber numbers. In addition, this paper presents, based on feed-forward backpropagation neural network theory, a method aiming to perform an identification of the vibrational pattern minimizing the error for further pratical applications. Neural networks are computational models inspired by an animal’s central nervous systems which is capable of pattern recognition in this case. A learning algorithm is produced based on information given and different wheights are adjusted-simulating neurons-becoming able to approximate non-linear functions. The method used, backpropagation, is a supervised learning method, and is a generalization of the delta rule. It requires a dataset of the desired output for many inputs, making up the training set. In the context of this work, the training have been composed of different values of Reynolds and Weber numbers, amplitude of the excitation pressure and vibrational pattern. Under these conditions, four different vibrational patterns were identified. The results of this works may lead to different combination of neuron numbers, trainning epochs and activation transfer function that can create a very good recognition method.