University of Sussex
Browse

File(s) not publicly available

Application of a generalised Levy residence time problem to neuronal dynamics

journal contribution
posted on 2023-06-07, 13:46 authored by David Waxman, J. F. Feng
The distribution of bursting lengths of neuron spikes, in a two-component integrate-and-fire model, is investigated. The stochastic process underlying this model corresponds to a generalisation of the Brownian motion underlying Levy's arcsine law of residence times. The generalisation involves the inclusion of a quadratic potential of strength ? and ? = 0 corresponds to Levy's original problem. In the generalised problem, the distribution of the residence times, T, over a time window t, is related to spectral properties of a complex, non-relativistic Hamiltonian of quantum mechanics. The distribution of T depends on ?t and varies from a U-shaped distribution for small ?t to a bell-shaped distribution for large ?t. The first two moments of T of the generalised problem are explicitly calculated and the crossover point between the two forms of the distribution is calculated. The distribution of residence times is shown to be independent of the magnitude of the stochastic force. This corresponds, in the neuron model, to exactly balanced synaptic inputs and, in this case, the distribution of residence times contains no information on synaptic inputs.

History

Publication status

  • Published

Journal

Europhysics Letters (EPL)

ISSN

0295-5075

Publisher

EDP Sciences

Issue

3

Volume

65

Page range

434

Department affiliated with

  • Biology and Environmental Science Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2007-02-14

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC