Publication details

Discrete Reaction-Dispersion Equation

Authors

POSPÍŠIL Zdeněk

Year of publication 2020
Type Article in Proceedings
Conference Difference Equations and Discrete Dynamical Systems with Applications
MU Faculty or unit

Faculty of Science

Citation
Web https://www.springer.com/gp/book/9783030355012
Doi http://dx.doi.org/10.1007/978-3-030-35502-9_14
Keywords diffusion; random walk; graph theory; stability of equilibria
Description The paper introduces a discrete analogy of the reaction-diffusion partial differential equation. Both the time and the space are considered to be discrete, the space is represented by a simple graph. The equation is derived from ``first principles''. Basic qualitative properties, namely, existence and stability of equilibria are discussed. The results are demonstrated on a particular system that can be interpreted as a model of metapopulation on interconnected patches with a deadly boundary. A condition for size of habitat needed for population survival is established.
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