Coherence and stochastic resonance in a delayed bistable system

Both coherence resonance (CR) and stochastic resonance (SR) in a delayed bistable system driven by additive and multiplicative white noises and a weak harmonic excitation are studied by using the theory of two-state model. For the weak noise intensity and delayed feedback, the analytic expressions of power-spectrum and linear-spectrum amplification are derived to quantify the CR and the SR, respectively. The study shows that the peak in the power spectrum at the frequency corresponding to the time delay attains the maximum for an appropriate amount of additive noise intensity and the CR manifests. The feedback gain plays an important role in the SR. For example, the positive feedback gain enhances the SR, but the negative feedback gain suppresses the system output and makes the SR disappear. Moreover, the system also exhibits the frequency SR.