Coherent stochastic resonance in a sextic double-well potential

Abstract

We study the response of a stochastic system described by the one-dimensional Fokker–Planck equation with a sextic double-well potential U 6( x)=(− c 4 x 4+ c 6 x 6) to a weak sinusoidal periodic signal. Two types of boundary conditions have been investigated: (i) absorbing boundary conditions, and (ii) natural boundary conditions. The unperturbed propagators are calculated by the eigenfunction-expansion method. We find that for case (i), the mean survival time shows the coherent stochastic resonance, and for case (ii), the signal-to-noise ratio exhibits the stochastic resonance. The results are compared with those of the bistable quartic double-well potential U 4(x)=(− 1 2 x 2+ 1 4 x 4) .