STABLE QUASI-PERIODIC ORBITS OF A CLASS OF QUINTIC DUFFING SYSTEMS

. For a Duffing-type oscillator with constant damping, a unique odd nonlinearity, and time-dependent coefficients which are quasi-periodic, we prove existence and stability conditions of quasi-periodic solutions. We thus generalize some results for periodic coefficients and quintic nonlinearity. We use the classical theory of perturbations and present some numerical examples for the quintic case to illustrate our findings.

Automated summary

In this paper, we investigate the existence and stability conditions of quasi-periodic solutions for a Duffing-type oscillator with constant damping, a unique odd nonlinearity, and time-dependent coefficients which are quasi-periodic. We extend some previous results for periodic coefficients and quintic nonlinearity. By using the classical theory of perturbations, we provide numerical examples for the quintic case to illustrate our findings.