The Mean First Passage Time of the Stochastic Resonance Driven by Dual-Sequence-Frequency-Hopping Signal and Noise

Abstract

The mean first passage time (MFPT) represents the dynamic characteristic of stochastic resonance (SR). The study focuses on how can the Dual-Sequence-Frequency-Hopping (DSFH) signal influence the MFPT and any difficulty in solving the MFPT problem considering the DSFH signal. In this current study, the SR system driven by DSFH signal and Gaussian white noise is described with the parameters of the signal amplitude, the frequency of Intermediate Frequency (IF) of the receptive DSFH signal, the SR system parameter, scale transformation coefficient, the noise intensity, and the sampling multiple, firstly. Secondly, under the assumption that MFPT is small aqueous about the domain of 0, the nonautonomous differential equation with MFPT is transformed to a nonhomogeneous differential equation with one unknown variable coefficient of second order. Finally, the numerical solution of MFPT can be obtained by the method of Runge–Kutta. Theoretical and simulation results are shown as below: (1) the effect of the signal amplitude, the IF frequency, the noise intensity, the SR system parameter, and the scale transformation coefficient, for decrease the MFPT, are positive; however, the effect of the sampling multiple is negative; (2) the MFPT cannot follow the dynamic period of the SR controlled by the IF frequency, when SNR is low; (3) when SNR = −12 dB, the sampling multiple is 200, the IF frequency is 2100, and the duty cycle reaches 25% (available for DSFH signal detection with peek or valley decision Liu et al. (2019)), so we need to decrease the IF frequency or increase the SNR for further availability.