Stochastic resonance for a time-delayed fractional nonlinear system driven by square-wave signal and dichotomous noise

The stochastic resonance (SR) phenomenon for a time-delayed fractional nonlinear system subjected to multiplicative and additive noise excited by square-wave signal and dichotomous noise is investigated. By virtue of generalized harmonic function technique, applying small delay approximation and adiabatic approximation, the system output signal-to-noise (SNR) is deduced. The research result shows that double SR phenomenon occurs when the SNR varies with the fractional exponent and with the strengths of the multiplicative and additive noise. One resonance peak appears when the SNR changes with the damping coefficient and with the delay time.