### Research - Coherence resonance in single neuron models

**Collaborators:**

Stefano Luccioli, Alessandro Torcini

**Description:**

The
topic of these studies are simulations of neuronal models (such as the
FitzHugh-Nagumo or the Hodgkin-Huxley model) under the influence of
noise. Typically the regularity of the neuronal response is analyzed
depending on the amount of noise and on the correlation strength.
Coherence resonance (CR) refers to a maximum of regularity for
intermediate parameter values while double coherence resonance (DCR)
denotes a (absolute) maximum coherence in the output occurring for an
optimal combination of noise variance and correlation. In the figure
below (FitzHugh-Nagumo model, regularity versus correlation and noise
strength) this is illustrated for both excitatory (e) and inhibitory
(i) correlation. The white squares mark the position of the excitatory
and the inhibitory DCR, respectively (for details see Ref. **[2]** below).

**Publications:**

**[4]** Kreuz T, Luccioli S, Torcini A:

Coherence Resonance due to correlated noise in neuronal models.

*Neurocomputing* **70**, 1970 (2007) [PDF].

**Abstract:**We study the regularity of noise-induced excitations in the FitzHugh-Nagumo (FHN) neuronal model subject to excitatory and inhibitory high-frequency input with and without correlations. For each value of the correlation a relative maximum of spike coherence can be observed for intermediate noise strengths (coherence resonance). Moreover, the FHN system exhibits an absolute maximum of coherent spiking for intermediate values of both the noise amplitude and the strength of correlation (double coherence resonance). The underlying mechanisms can be explained by means of the discrete input statistics.

**[3]** Torcini A, Luccioli S, Kreuz T:

Coherent Response of the Hodgkin-Huxley neuron in the high input regime.

*Neurocomputing* **70**, 1943 (2007).

**[2]** Kreuz T, Luccioli S, Torcini A:

Double coherence resonance in neuron models driven by discrete correlated noise.

*Phys Rev Lett* **97**, 238101 (2006) [PDF].

**Abstract:**We study the influence of correlations among discrete stochastic excitatory or inhibitory inputs on the response of the FitzHugh-Nagumo neuron model. For any level of correlation, the emitted signal exhibits at some finite noise intensity a maximal degree of regularity, i.e., a coherence resonance. Furthermore, for either inhibitory or excitatory correlated stimuli, a double coherence resonance is observable. Double coherence resonance refers to a (absolute) maximum coherence in the output occurring for an optimal combination of noise variance and correlation. All of these effects can be explained by taking advantage of the discrete nature of the correlated inputs.

**[1]** Luccioli S, Kreuz T, Torcini A:

Dynamical response of the Hodgkin-Huxley model in the high-input regime.

*Phys Rev E* **73**, 041902 (2006).