L{\'e}vy-noise-induced wavefront propagation for bistable systems

Abstract

The influence of the L{\'e}vy noise's properties on wavefront propagation is analyzed on examples of ensembles of locally coupled bistable oscillators and a single bistable delayed-feedback oscillator considered as a spatially-extended system evolving in quasi-space. It is shown that additive L{\'e}vy noise allows to induce wavefront propagation in ensembles of symmetric bistable oscillators. In such a case, the direction and velocity of the noise-sustained propagation is determined both by the noise's skewness parameter and by the coupling topology (bidirectional and unidirectional coupling schemes are distinguished). In addition, additive L{\'e}vy noise induces wavefront propagation in a bistable delayed-feedback oscillator assumed to be symmetric such that its dynamics replicates the collective behaviour in the ensemble with unidirectional coupling. The wavefront propagation velocity used in this analysis is shown to be varied when adjusting the noise parameters. The revealed effects are demonstrated in the ensembles by using numerical simulation, whereas the numerical exploration of the delayed-feedback oscillator is complemented by physical experiments, showing a good correspondence and disclosing thereby the robustness of the observed phenomena.