{
  "id": "math/0612574",
  "version": "v1",
  "published": "2006-12-20T20:12:21.000Z",
  "updated": "2006-12-20T20:12:21.000Z",
  "title": "Coarse-grained dynamics of an activity bump in a neural field model",
  "authors": [
    "C. R. Laing",
    "T. A. Frewen",
    "I. G. Kevrekidis"
  ],
  "comment": "Corrected aknowledgements",
  "doi": "10.1088/0951-7715/20/9/007",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study a stochastic nonlocal PDE, arising in the context of modelling spatially distributed neural activity, which is capable of sustaining stationary and moving spatially-localized ``activity bumps''. This system is known to undergo a pitchfork bifurcation in bump speed as a parameter (the strength of adaptation) is changed; yet increasing the noise intensity effectively slowed the motion of the bump. Here we revisit the system from the point of view of describing the high-dimensional stochastic dynamics in terms of the effective dynamics of a single scalar \"coarse\" variable. We show that such a reduced description in the form of an effective Langevin equation characterized by a double-well potential is quantitatively successful. The effective potential can be extracted using short, appropriately-initialized bursts of direct simulation. We demonstrate this approach in terms of (a) an experience-based \"intelligent\" choice of the coarse observable and (b) an observable obtained through data-mining direct simulation results, using a diffusion map approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-20T20:12:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "neural field model",
      "activity bump",
      "coarse-grained dynamics",
      "spatially distributed neural activity",
      "stochastic nonlocal pde"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}