{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "GAJDYXNHN2"
    }
  ],
  "body": "\n## Summary\n\nFisher's equation, also called the KPP–Fisher equation, is the scalar [[reaction–diffusion equation|TAAHWE917M]] $u_t = D u_{xx} + r u(1 - u)$.\nIt couples diffusion with logistic growth.\nIt was proposed by Fisher in 1937 for the spread of an advantageous gene, and studied in the same year by Kolmogorov, Petrovsky and Piskunov.\nIt is the model example of an equation with [[travelling wave|M37M411KP7]] fronts that invade an unstable state.\n\n## Explanations\n\n### L1 human\n\nThink of a population that spreads by random motion and grows until it reaches the carrying capacity $1$.\nWhere $u$ is near $0$ the population grows, and diffusion pushes it into empty space.\nThe result is a front that moves at constant speed, with the full state $u = 1$ behind it and the empty state $u = 0$ ahead.\nWith $D = r = 1$, the slowest such front has speed $2$.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "35K57",
      "35K58",
      "35Q92"
    ],
    "name": "Fisher's equation",
    "same_as": {
      "wikidata": "Q1763840",
      "wikipedia": "KPP–Fisher equation"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/KPP%E2%80%93Fisher_equation"
      }
    ],
    "specializes": [
      "TAAHWE917M"
    ],
    "tag": "AXV2PH7FEZ"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/AXV2PH7FEZ/",
  "links": [
    {
      "field": "specializes",
      "target": "TAAHWE917M"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/AXV2PH7FEZ.md",
  "msc": [
    "35K57",
    "35K58",
    "35Q92"
  ],
  "name": "Fisher's equation",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/AXV/AXV2PH7FEZ.md",
  "status": null,
  "tag": "AXV2PH7FEZ",
  "uri": "m2://AXV2PH7FEZ",
  "url": "https://tamnd.github.io/math2/wiki/fishers-equation/",
  "writing": {
    "tag": "AXV2PH7FEZ",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}