Qualitative analysis of a mechanical system of coupled nonlinear oscillators

Abstract

In this paper we investigate nonlinear systems of second order ODEs describing the dynamics of two coupled nonlinear oscillators of a mechanical system. We obtain, under certain assumptions, some stability results for the null solution. Also, we show that in the presence of a time-dependent external force, every solution starting from sufficiently small initial data and its derivative are bounded or go to zero as the time tends to $+\infty$, provided that suitable conditions are satisfied. Our theoretical results are illustrated with numerical simulations.

Keywords

• coupled oscillators
• uniform stability
• asymptotic stability
• uniform asymptotic stability