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The response of subdiffusive bistable fractional Fokker–Planck systems to rectangular signals

We study the response of one-dimensional subdiffusive fractional Fokker–Planck systems with a general confining potential, when it is perturbed from its stationary state by a time-dependent non-sinusoidal driving force. Three types of rectangular driving signals have been investigated: a rectangular pulse, a periodic telegraph signal and a generalized telegraph signal with a fractional duty cycle. We derive analytic expressions for the linear response and the input energy in one period of the driving signal. In particular, for signals with a long period, we obtain several asymptotic results concerning the wave form of the response and the stochastic energetics. Numerical results for representative symmetric, as well as asymmetric, subdiffusive bistable systems are presented and discussed.