**Appendix A. Single-DOF Oscillator**

*Appendix A.1. Equations of Motion*

$$\text{Using } \omega\_{\mathbf{n}} = \sqrt{\frac{k}{m'}}, \mathfrak{f} = \frac{c}{2\sqrt{km'}}, \mathfrak{x}\_0 = \frac{\mathbf{\tilde{x}}}{\mathbf{\tilde{k}}}, \text{and } \mathfrak{r} = \omega\_{\mathbf{n}}t, \frac{\mathbf{d}}{dt} = \omega\_{\mathbf{n}}\frac{\mathbf{d}}{d\tau} \text{ we re-write Equation (5) into}$$

$$\mathfrak{F} + 2\mathfrak{f}\mathfrak{k} + \mathfrak{x} = \mathfrak{F} \tag{A1}$$

where (˜·) indicates a non-dimensional quantity.

*Appendix A.2. Convergence of Basin Stability Values*

The number of samples *n* is varied to answer the question of how many samples from Q are required for a robust approximation of the basin stability values. Figure A1 displays the convergence of the basin stability values for the single-DOF oscillator case and the corresponding analytical values.

**Figure A1.** Effect of increasing the number of samples for estimating the basin stability values at *v*˜<sup>d</sup> = 1.5. For each value *n*, the calculation has been repeated ten times. Mean values *δ* and the standard deviation *σ* are reported along with the analytical values.
