Deterministic force-free resonant activation

The combined action of noise and deterministic force in dynamical systems can induce resonant effects. Here, we demonstrate a minimal, deterministic force-free setup allowing for the occurrence of resonant, noise-induced effects. We show that in the archetypal problem of escape from finite intervals driven by α-stale noise with a periodically modulated stability index, depending on the initial direction of the modulation, resonant-activation-like or noise-enhanced-stability-like phenomena can be observed. Consequently, in comparison to traditional Lévy flights, Lévy flights with a time-dependent jump length exponent are capable of facilitating or slowing down the escape from finite intervals in an analogous way, such as the modulation of the potential in the resonant activation setup. (paper)