{
  "id": "1912.09762",
  "version": "v1",
  "published": "2019-12-20T11:17:35.000Z",
  "updated": "2019-12-20T11:17:35.000Z",
  "title": "Neural Field Models with Transmission Delays and Diffusion",
  "authors": [
    "Len Spek",
    "Yuri A. Kuznetsov",
    "Stephan A. van Gils"
  ],
  "categories": [
    "math.DS",
    "math.FA"
  ],
  "abstract": "A neural field models the large scale behaviour of large groups of neurons. We extend results of Van Gils et al. [2013] and Dijkstra et al. [2015] by including a diffusion term into the neural field, which models direct, electrical connections. We extend known and prove new sun-star calculus results for delay equations to be able to include diffusion and explicitly characterise the essential spectrum. For a certain class of connectivity functions in the neural field model, we are able to compute its spectral properties and the first Lyapunov coefficient of a Hopf bifurcation. By examining a numerical example, we find that the addition of diffusion suppresses non-synchronised steady-states, while favouring synchronised oscillatory modes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-20T11:17:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "neural field model",
      "transmission delays",
      "sun-star calculus results",
      "large scale behaviour",
      "first lyapunov coefficient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}