title: Resonances and noise in a stochastic Hindmarsh-Rose model of thalamic neurons.
abstract: Thalamic neurons exhibit subthreshold resonance when stimulated with small sine wave signals of varying frequency and stochastic resonance when noise is added to these signals. We study a stochastic Hindmarsh-Rose model using Monte-Carlo simulations to investigate how noise, in conjunction with subthreshold resonance, leads to a preferred frequency in the firing pattern. The resulting stochastic resonance (SR) exhibits a preferred firing frequency that is approximately exponential in its dependence on the noise amplitude. In similar experiments, frequency dependent SR is found in the reliability of detection of alpha-function inputs under noise, which are more realistic inputs for neurons. A mathematical analysis of the equations reveals that the frequency preference arises from the dynamics of the slow variable. Noise can then transfer the resonance over the firing threshold because of the proximity of the fast subsystem to a Hopf bifurcation point. Our results may have implications for the behavior of thalamic neurons in a network, with noise switching the membrane potential between different resonance modes.
authors.affiliation: Department of Mathematics, Institute of Applied Mathematics, University of British Columbia, Vancouver, Canada BC V6T 1Z2. reinker@math.ubc.ca
authors.forename: Stefan
authors.initials: S
authors.lastname: Reinker
authors.forename: Ernest
authors.initials: E
authors.lastname: Puil
authors.forename: Robert M
authors.initials: RM
authors.lastname: Miura
mesh_terms: D000200:Action Potentials; D000818:Animals; D003198:Computer Simulation; D006801:Humans; D008959:Models, Neurological; D009010:Monte Carlo Method; D009415:Nerve Net / Q000502:physiology; D009474:Neurons / Q000502:physiology*; D009716:Numerical Analysis, Computer-Assisted; D013269:Stochastic Processes; D009435:Synaptic Transmission / Q000502:physiology; D013788:Thalamus / Q000502:physiology*