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 Lvy flights, Lvy 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.

噪声和确定性力在动力系统中的共同作用会引起共振效应。在这里，我们演示了一种最小的确定性无力设置，允许发生共振的，噪声引起的影响。我们表明，在原型问题中，由具有周期性调制稳定性指标的α-陈旧噪声驱动的有限区间逃逸，取决于调制的初始方向，可以像共振激活一样或像噪声增强一样。观测到的。因此，与传统的Lvy飞行相比，具有随时间变化的跳跃长度指数的Lvy飞行能够以类似的方式来促进或减慢从有限间隔的逃逸，例如在共振激活装置中调节电势。