Noise can assist neurons in the detection of weak signals via a mechanism known as stochastic resonance (SR). In a previous study [Phys. Lett. A 243, 281 (1998)], we showed that when colored noise with ${1/f}^{\beta }$ spectrum is added to the FitzHugh-Nagumo (FHN) neuronal model, the optimal noise variance for SR could be minimized with $\beta \approx 1.$ In this study, we investigate analytically how the noise color $\left(\beta \right)$ affects the SR profile in a linearized version of the FHN model. We demonstrate that the aforementioned effect of $1/f$ noise is related to the dynamical characteristics of the model neuron, i.e., the refractory period, the low-pass filtering effect of the membrane capacitance, and the high-pass filtering effect of the recovery variable.

• Received 31 March 1999

DOI:https://doi.org/10.1103/PhysRevE.60.4637