Resonances and noise in a stochastic Hindmarsh-Rose model of thalamic neurons |
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| Authors: | Reinker Stefan Puil Ernest Miura Robert M |
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| Institution: | (1) Department of Mathematics, Institute of Applied Mathematics, University of British Columbia, Vancouver, Canada, BC, V6T 1Z2;(2) Department of Pharmacology & Therapeutics, University of British Columbia, Vancouver, Canada, BC, V6T 1Z3;(3) Departments of Mathematical Sciences and Biomedical Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA;(4) Departments of Mathematics and Pharmacology & Therapeutics, Institute of Applied Mathematics, University of British Columbia, Vancouver, Canada, BC, V6T 1Z2;(5) Present address: Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA |
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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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