Inhibition of rhythmic neural spiking by noise: the occurrence of a minimum in activity with increasing noise |
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Authors: | Boris S Gutkin Jürgen Jost Henry C Tuckwell |
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Institution: | (1) Group for Neural Theory, Departément des Etudes Cognitives, Ecole Normale Supérieure, 3 rue d’Ulm, 75005 Paris, France;(2) Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany |
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Abstract: | The effects of noise on neuronal dynamical systems are of much current interest. Here, we investigate noise-induced changes
in the rhythmic firing activity of single Hodgkin–Huxley neurons. With additive input current, there is, in the absence of
noise, a critical mean value μ = μ
c above which sustained periodic firing occurs. With initial conditions as resting values, for a range of values of the mean
μ near the critical value, we have found that the firing rate is greatly reduced by noise, even of quite small amplitudes.
Furthermore, the firing rate may undergo a pronounced minimum as the noise increases. This behavior has the opposite character
to stochastic resonance and coherence resonance. We found that these phenomena occurred even when the initial conditions were
chosen randomly or when the noise was switched on at a random time, indicating the robustness of the results. We also examined
the effects of conductance-based noise on Hodgkin–Huxley neurons and obtained similar results, leading to the conclusion that
the phenomena occur across a wide range of neuronal dynamical systems. Further, these phenomena will occur in diverse applications
where a stable limit cycle coexists with a stable focus. |
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Keywords: | Neuronal dynamics Hodgkin– Huxley model Stochastic processes Inverse stochastic resonance |
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