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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 1: 11-25. doi: 10.3934/mbe.2014.11.11
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Diffusion approximation of neuronal models revisited

  • 1.
    Institute of Physiology, Academy of Sciences of the Czech Republic, Videnska 1083, 142 20 Prague 4
  • Received: 01 December 2012 Accepted: 29 June 2018 Published: 01 September 2013

  • MSC : 60J60, 60J70, 92C20.

  • Leaky integrate-and-fire neuronal models with reversal potentials have a number of different diffusion approximations, each depending on the form of the amplitudes of the postsynaptic potentials.Probability distributions of the first-passage times of the membrane potential in the original model and itsdiffusion approximations are numerically compared in order to find whichof the approximations is the most suitable one.The properties of the random amplitudes of postsynapticpotentials are discussed.It is shown on a simple example that the quality of the approximation depends directly on them.

    Citation: Jakub Cupera. Diffusion approximation of neuronal models revisited[J]. Mathematical Biosciences and Engineering, 2014, 11(1): 11-25. doi: 10.3934/mbe.2014.11.11

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  • Leaky integrate-and-fire neuronal models with reversal potentials have a number of different diffusion approximations, each depending on the form of the amplitudes of the postsynaptic potentials.Probability distributions of the first-passage times of the membrane potential in the original model and itsdiffusion approximations are numerically compared in order to find whichof the approximations is the most suitable one.The properties of the random amplitudes of postsynapticpotentials are discussed.It is shown on a simple example that the quality of the approximation depends directly on them.


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    3. Massimiliano Tamborrino, Petr Lansky, Shot noise, weak convergence and diffusion approximations, 2021, 418, 01672789, 132845, 10.1016/j.physd.2021.132845
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