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Resonances and noise in a stochastic Hindmarsh-Rose model of thalamic neurons

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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.

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Author notes

  1. Robert M. Miura

    Present address: Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ, 07102, USA

Authors and Affiliations

  1. Department of Mathematics, Institute of Applied Mathematics, University of British Columbia, Vancouver, Canada, BC, V6T 1Z2

    Stefan Reinker

  2. Department of Pharmacology & Therapeutics, University of British Columbia, Vancouver, Canada, BC, V6T 1Z3

    Ernest Puil

  3. Departments of Mathematical Sciences and Biomedical Engineering, New Jersey Institute of Technology, Newark, NJ, 07102, USA

    Robert M. Miura

  4. Departments of Mathematics and Pharmacology & Therapeutics, Institute of Applied Mathematics, University of British Columbia, Vancouver, Canada, BC, V6T 1Z2

    Robert M. Miura

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  1. Stefan Reinker
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  2. Ernest Puil
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  3. Robert M. Miura
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Correspondence to Robert M. Miura.

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Reinker, S., Puil, E. & Miura, R.M. Resonances and noise in a stochastic Hindmarsh-Rose model of thalamic neurons. Bull. Math. Biol. 65, 641–663 (2003). https://doi.org/10.1016/S0092-8240(03)00026-0

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  • DOI: https://doi.org/10.1016/S0092-8240(03)00026-0

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