Linear response and stochastic resonance of subdiffusive bistable fractional Fokker–Planck systems

By the method of eigenfunction expansion, we study the linear response to a time-dependent external field for stochastic systems described by the one-dimensional subdiffusive fractional Fokker–Planck equation with a general confining potential and natural boundary conditions; an expression for the response function is derived. For a sinusoidal driving force, we obtain expressions for the amplitude and phase lag of the response, the input energy per period, and the signal-to-noise ratio. We have also studied the perturbing effect due to fluctuations in the diffusion coefficient. Numerical results for representative symmetric, as well as asymmetric, bistable systems with different degrees of subdiffusiveness are presented and discussed.