Qualitative analysis of a mechanical system of coupled nonlinear oscillators

Moroșanu, Gheorghe and Vladimirescu, Cristian (2023) Qualitative analysis of a mechanical system of coupled nonlinear oscillators. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2023 (16). pp. 1-26. ISSN 1417-3875

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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 +∞, provided that suitable conditions are satisfied. Our theoretical results are illustrated with numerical simulations.

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