Dynamics of cubic–quintic nonlinear [formula omitted]-symmetry mechanical oscillators

Abstract

In this paper, we investigate the dynamics of two mechanical coupled oscillators (MCO) with Parity-Time (PT)-symmetry i.e., one has gain and the other has an equal and opposite amount of loss. In the linear case, the eigenmodes and breaking points were determined. In the nonlinear case, the breaking point for soft cubic or quintic potential obtained numerically was also found analytically with perfect agreement. However, instead of the breaking point, for the hard cubic or quintic potential, it is noted a transition toward a regime of periodic or quasi-periodic stable oscillation with energy transfer from the loss oscillator to the gain oscillator. This latter result suggests very important applications within the framework of the optical cavities and waveguides.