Transitory stabilization of unstable states with lévy processes

Abstract

Some dynamic systems operate at a critical point between stability and instability requiring fine tuning of parameters. In addition, abnormal fluctuation phenomena could be associated with the prolongation of the life times of transiently stabilized unstable states. This work is focused on knowing and identifying the effects introduced by Lévy processes with diverse properties, particularly superdiffusive and truncated. Numerically, the effect of parametric random perturbations on an unstable archetype system is analyzed and it is found that extreme fluctuations with truncated Lévy probability distributions postpone the decay of unstable states. An analysis of the escape process based on the theory of large fluctuations provides an alternative way to characterize the response of the system under disturbances.