Stability for systems of 1-D coupled nonlinear oscillators. (June 2021) - Moroşanu, Gheorghe; Vladimirescu, Cristian
Abstract: The stability of the null solution of different systems of differential equations describing the motion of 1-D coupled nonlinear oscillators is discussed. Under certain assumptions we derive some stability results. Specifically, in the case of coupled damped oscillators we obtain asymptotic stability of the null solution (see Theorem 3.1, Example 3.1, and Fig. 2 ), while in the case of partial lack of damping we only obtain convergence to zero of the solution components corresponding to damped oscillators (see Theorem 4.1, Example 4.1, and Fig. 5 ). In all cases, including the case of coupled undamped oscillators, we obtain uniform stability of the null solution.