Energy dissipation in a nonlinearly damped Duffing oscillator

In this paper, we study the effect of including a nonlinear damping term proportional to the power of the velocity in the dynamics of a double-well Duffing oscillator. In particular, we focus our attention in understanding how the energy dissipates over a cycle and along the time, by the use of different tools of analysis. Analytical and numerical results for different damping terms are shown, and the presence of a discontinuity and an inversion of behavior depending on the initial energy are discussed. An averaged power loss in a period is defined, showing similar characteristics as the energy dissipation over a cycle, although no discontinuity is present. The discontinuity gap which appears for the energy dissipation at a certain value of the initial energy decreases as the power of the damping term increases and an associated scaling law is found.