Effects of small time delay on a bistable system subject to Levy stable noise

Levy stable noise is often used to describe impulsive noise bursting in communication systems. This paper investigates the effects of small time delay on a bistable system driven by an aperiodic bipolar pulse signal and Levy stable noise. We obtain the dynamical probability density of the system response by solving the approximated time-delayed fractional Fokker-Planck equation (FFPE) via an implicit finite difference method. A new approach to evaluate the system response time is presented. The bit error rate (BER) is employed to measure the performance of the bistable system in detecting binary signals. The theoretical BER is validated by the Monte-Carlo simulation. We find that the existence of time delay can change both the drift term and the diffusion coefficient in time-delayed FFPE. For small noise intensity, the time delay extends the system response time and thus reduces the detection performance. However, effects of this kind will fade away with the increase of noise intensity.