Dynamique de l'oscillateur salin sous excitation sinusoïdale et de bruit borné

Abstract

The work in this thesis is based on the saline oscillator in the presence of a harmonic and bounded noise excitation. For this purpose, the system is modeled by a di erential system of the Filippov type. We study the dynamics and stability of the single system as well as the synchronisation in the coupled case. The response of the model is evaluated as well as the e ect of the parameters of the excitation, namely its amplitude and frequency, on the response of the model. It is found that the amplitude of the exciter signi cantly determines the amplitude of the system response, while inuencing the observed unidi rectional synchronisation mode. Through numerical simulations, we nd that over a wide range of excitation parameters, the oscillator exhibits a period T of oscillation whose am plitude increases with the amplitude of the exciter. Furthermore, the model shows mainly sub-harmonic and quasi-harmonic oscillations, these depending on the values of the exci tation amplitude and frequency. The harmonic balance method is then used to check the shape of the amplitude dependence on the excitation parameters. A study of the stability of the oscillatory mode is then considered using the evaluation of the largest Lyapunov exponent in order to determine in which parameter regime chaotic behaviour would occur. It is found that the periodically excited salt oscillator exhibits regular oscillations in the admissible parameter regime. Using the stochastic averaging method and Monte Carlo simulations, the probabilistic response of the oscillator under bounded noise excitation is determined. The Fokker-Planck-Kolmogorov equations are established, so the statistical response at steady state is a probability density. We nd that bounded noise excitation a ects the oscillation period, midpoint and amplitude.