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Fakultät für Mathematik
Anne Kandler, Roman Unger: Population dispersal via diffusion-reaction equations

Anne Kandler, Roman Unger: Population dispersal via diffusion-reaction equations


Author(s):
Anne Kandler
Roman Unger
Title:
Anne Kandler, Roman Unger: Population dispersal via diffusion-reaction equations
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 16, 2010
Mathematics Subject Classification:
92D25 [Population dynamics (general) ]
65M60 [Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods ]
9201 [Instructional exposition (textbooks, tutorial papers, etc.)]
Abstract:
Diffusion-reaction systems are well-established in different life-science disciplines. When applied to 'human questions' they are used to estimate the demographic processes involved in major human (or animal) dispersal episodes and to estimate the general spread pattern of new ideas or technologies through cultures. This manuscript gives an introduction to diffusion-reaction systems for a non-mathematical audience. We focus on describing dispersal processes and start with modelling and analysing the spread dynamic of a single population under different dispersal and growth hypotheses. Further, we focus on the impacts of population interactions on spread behaviour of a particular population. Lastly we introduce an open software package 'CultDiff' which provides a solution tool for diffusion reaction systems.
Keywords:
Population dispersal, population growth, diffusion-reaction system, random walk, Lotka-Volterra system, CultDiff
Language:
English
Publication time:
08/2010

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