Discrete Reaction-Dispersion Equation

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

Faculty of Science

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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