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
