  Nonlinear oscillators are a key modelling tool in many applications. The
influence of annealed noise on nonlinear oscillators has been studied
intensively. It can induce effects in nonlinear oscillators not present in the
deterministic setting. Yet, there is no theory regarding the quenched noise
scenario of random parameters sampled on fixed time intervals, although this
situation is often a lot more natural. Here we study a paradigmatic nonlinear
oscillator of van-der-Pol/FitzHugh-Nagumo type under quenched noise as a
piecewise-deterministic Markov process. There are several interesting effects
such as period shifts and new different trapped types of small-amplitude
oscillations, which can be captured analytically. Furthermore, we numerically
discover quenched resonance and show that it differs significantly from
previous finite-noise optimality resonance effects. This demonstrates that
quenched oscillatorscan be viewed as a new building block of nonlinear
dynamics.
