Stochastic resonance in overdamped systems with fractional power nonlinearity

The stochastic resonance phenomenon in overdamped systems with fractional power nonlinearity is thoroughly investigated. The first kind of nonlinearity is a general fractional power function. The second kind of nonlinearity is a fractional power function with deflection. For the first case, the response is clearly divergent for some fractional exponent values. The curve of the spectral amplification factor versus the fractional exponent presents some discrete regions. For the second case, the response will not be divergent for any fractional exponent value. The spectral amplification factor decreases with the increase in the fractional exponent. For both cases, the nonlinearity is the necessary ingredient to induce stochastic resonance. However, it is not the sufficient cause to amplify the weak signal. On the one hand, the noise cannot induce stochastic resonance in the corresponding linear system. On the other hand, the spectral amplification factor of the nonlinear system is lower than that of the corresponding linear system. Through the analysis carried out in this paper, we are able to find that the system with fractional deflection nonlinearity is a better stochastic resonance system, especially when an appropriate exponent value is chosen. The results in this paper might have a certain reference value for signal processing problems in relation with the stochastic resonance method.