Dynamics of Cubic-Quintic Nonlinear Pt-Symmetry Mechanical Oscillators

In this paper, we investigate the dynamic 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 linear limit and with the hard/soft Duffing cubic or quintic nonlinearities. In the linear regime, we find the eigenvalues and determine the PT-symmetry breaking threshold point (BTP). In the nonlinear level, the Hamilton function is derived and the stability of the different branches of fixed points (FP) found is analyzed. The numerical treatment shows that the stability of the system depends on the nonlinearity and the initial conditions. The analytical approach reveals that the stability is governed by the eigenfrequencies of the system. Correspondences are found between the numerical and the analytical results.