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@inproceedings{1646078, author = {Pospíšil, Zdeněk}, address = {Cham, Switzerland}, booktitle = {Difference Equations and Discrete Dynamical Systems with Applications}, doi = {http://dx.doi.org/10.1007/978-3-030-35502-9_14}, editor = {M. Bohner, S. Siegmund, R. Šimon Hilscher, P. Stehlík}, keywords = {diffusion; random walk; graph theory; stability of equilibria}, howpublished = {tištěná verze "print"}, language = {eng}, location = {Cham, Switzerland}, isbn = {978-3-030-35501-2}, pages = {323-333}, publisher = {Springer}, title = {Discrete Reaction-Dispersion Equation}, url = {https://www.springer.com/gp/book/9783030355012}, year = {2020} }
TY - JOUR ID - 1646078 AU - Pospíšil, Zdeněk PY - 2020 TI - Discrete Reaction-Dispersion Equation PB - Springer CY - Cham, Switzerland SN - 9783030355012 KW - diffusion KW - random walk KW - graph theory KW - stability of equilibria UR - https://www.springer.com/gp/book/9783030355012 L2 - https://www.springer.com/gp/book/9783030355012 N2 - 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. ER -
POSPÍŠIL, Zdeněk. Discrete Reaction-Dispersion Equation. In M. Bohner, S. Siegmund, R. Šimon Hilscher, P. Stehlík. \textit{Difference Equations and Discrete Dynamical Systems with Applications}. Cham, Switzerland: Springer, 2020, p.~323-333. ISBN~978-3-030-35501-2. Available from: https://dx.doi.org/10.1007/978-3-030-35502-9\_{}14.
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