Sample notebook on integrating numerically the Fisher-Kolmogorov equation in 1 dimension:

The Fisher-Kolmogorov equation,

• J.D. Murray: Mathematical Biology I & II (Springer, 2002)
• N.F. Britton: Essential Mathematical Biology ( Springer, 2003).
• R.S. Cantrell & C. Cosner: Spatial Ecology via Reaction-Diffusion Equations (Wiley, 2003).
• A. Okubo & S.A. Levin: Diffusion and Ecological Problems (Springer, 2001).
• P. Turchin: Quantitative Analysis of Movement (Sinauer, 1998)
• Skellam, J.G., 1951. Random dispersal in theoretical populations. Biometrika, 38: 196-218.

• Reaction-diffusion tutorial: from the point of view of chemistry, nice videos.
• Gray-Scott model: great site with codes, theory and results of a simple chemical reaction-diffusion that generates very complicated patterns. Also link to relevant paper on pattern generation by reaction-diffusion equations.

• Diffusion and home range parameters from rodent population measurements in Panama. Giuggioli et al. (2005). Bulletin of Mathematical Biology.

• Original paper
• in Wikipedia
• Aiming the “unreasonable effectiveness of mathematics” at ecological theory. Giznburg et al. (2007).