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Nonlinear systems with noise can display SR-like behavior even without external signal, this phenomenon has been called autonomous SR or coherence resonance (CR). It was first discussed in a simple autonomous system in the vicinity of the saddle-node bifurcation [31]. Recently it has attracted more interest in the excitable systems, e.g., the HH model [22], the Hindermarsh-Rose model, and the Plant model [32], the FitzHugh-Nagumo model [33]. In addition, CR has been observed in the experiment recently [34]. The nonuniform noise-induced limit cycle leads to a peak at a nonzero frequency (related to the main frequency of the oscillation) in the PSD. In most studies, the coherence of the system is characterized by a factor β measured from the PSD [see its definition in Eq. (9)], and it increases first to a maximum and then decrease as the intensity of noise increases, showing an optimization of the coherent limit cycle to the noise. It is argued that the existence of a subthreshold oscillation (e.g., a focus-type state of equilibrium) is a necessary condition to observe any peak in the PSD at a nonzero frequency.
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39
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33744861356
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note
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10(S/B) with S and B representing the signal peak and the mean amplitude of the background noise at the input signal frequency in the power spectrum density of V(t), respectively.
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