{"id":46451542,"url":"https://github.com/kunzaatko/reactivediffusion","last_synced_at":"2026-03-06T00:32:06.626Z","repository":{"id":246202183,"uuid":"820393483","full_name":"kunzaatko/ReactiveDiffusion","owner":"kunzaatko","description":"A report on the Fisher-KPP (Kolmogorov-Petrovsky-Piskunov) and the Allee-KPP equations with stading wave solutions. 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u)$\n- Logistic growth form: $F(u) = \\alpha u (1 - u/u_\\infty)$\n- Dimensionless form: $\\frac{\\partial u}{\\partial \\tau} = \\frac{\\partial^2 u}{\\partial \\chi^2} + u(1-u)$\n- Travelling wave ODE: $-c \\frac{du}{dz} = \\frac{d^2 u}{dz^2} + u(1-u)$\n\n### Allee Effect Equation\n- Reaction term: $F(u) = \\alpha u \\left(1 - \\frac{u}{u_\\infty}\\right)\\left(\\frac{u - u_-}{u_-}\\right)$\n- Dimensionless form: $\\frac{\\partial u}{\\partial \\tau} = \\frac{\\partial^2 u}{\\partial \\chi^2} + u (1 - u ) \\left(\\frac{u - u_-}{u_-}\\right)$\n\n## Figures\n\n\u003cp align=\"center\"\u003ePhase portrait of diffusion equation with the Fisher-KPP reactive term\u003cbr\u003e\u003cimg src=\"src/figs/phase-portrait-kpp-fisher.svg\" alt=\"Phase portrait Fisher-KPP\"\u003e\u003c/p\u003e\n\n\u003cp align=\"center\"\u003ePhase portrait of diffusion equation with the Allee effect reactive term\u003cbr\u003e\u003cimg src=\"src/figs/phase-portrait-kpp-allee.svg\" alt=\"Phase portrait Allee\"\u003e\u003c/p\u003e\n\n## Compilation \n\nThe document can be compiled using [`tectonic`](https://github.com/tectonic-typesetting/tectonic)\n```bash\n$ tectonic -X build\n```\nafter creating the figures.\n\nThe figures may be generated with `Julia` (tested version `1.10`) by running the scripts in `src/figs/`, e.g.\n```bash\n$ julia --project fisher_wave.jl\n```\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fkunzaatko%2Freactivediffusion","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fkunzaatko%2Freactivediffusion","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fkunzaatko%2Freactivediffusion/lists"}