  L\'evy noise is a paradigmatic noise used to describe out-of-equilibrium
systems. Typically, properties of L\'evy noise driven systems are very
different from their Gaussian white noise driven counterparts. In particular,
under action of L\'evy noise, stationary states in single-well, super-harmonic,
potentials are no longer unimodal. Typically, they are bimodal however for
fine-tuned potentials the number of modes can be further increased. The
multimodality arises as a consequence of the competition between long
displacements induced by the non-equilibrium stochastic driving and action of
the deterministic force. Here, we explore robustness of bimodality in the
quartic potential under action of the L\'evy noise. We explore various
scenarios of bounding long jumps and assess their ability to weaken and destroy
multimodality. In general, we demonstrate that despite its robustness it is
possible to destroy the bimodality, however it requires drastic reduction in
the length of noise-induced jumps.
