Fig. 1. Examples of non-linearizable systems.

a Snap-through instability of a microelectro-mechanical (MEMS) device with three coexisting equilibria (Sandia National Laboratories). b Wind-tunnel flutter of an airplane prototype, involving a fixed point and coexisting limit cycles (NASA Langley Research Center). c Swirling clouds behind an island in the Pacific ocean, forming a vortex street with coexisting isolated hyperbolic and elliptic trajectories for the dynamical system describing fluid particle motion (USGS/NASA). d Phase portrait of the damped, double-well Duffing oscillator $\ddot{x}+\dot{x}-x+\beta x^3=0$ with β > 0, the most broadly used model for nonlinear systems with coexisting domains of attraction (colored), such as the MEMS device in plot (a). e Nonlinear response amplitude ($\mid x\left(t\right){\mid }_{\max }$) in the forced-damped, single-well Duffing oscillator, $\ddot{x}+\dot{x}+x+\beta x^3=f\cos \omega t$ with β > 0, under variations of the forcing frequency ω and forcing amplitude f. Coexisting stable and unstable periodic responses show non-linearizable dynamics conclusively for this classic model.