Effects of Levy noise in aperiodic stochastic resonance

We present a Grunwald-Letnikov implicit finite difference method to solve the space-fractional Fokker-Planck equation with natural boundary condition. Then the properties of aperiodic stochastic resonance in the presence of Levy noise are investigated in theory and tested by simulation. It is shown that aperiodic stochastic resonance does occur in the presence of Levy noise, but is reduced by the lower Levy index alpha. With the optimal system parameters, the probability of detection error decreases with the decrease of a. Therefore, the performance of a bistable system is improved by the lower index a of Levy noise.