Abstract
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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Acknowledgements
This research was partially supported by the grant No. GA16-03796S of the Czech Grant Agency.
I am grateful to the both of the anonymous referees for their comments that allow to clarify the matter and to substantially improve the text.
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Pospíšil, Z. (2020). Discrete Reaction-Dispersion Equation. In: Bohner, M., Siegmund, S., Šimon Hilscher, R., Stehlík, P. (eds) Difference Equations and Discrete Dynamical Systems with Applications. ICDEA 2018. Springer Proceedings in Mathematics & Statistics, vol 312. Springer, Cham. https://doi.org/10.1007/978-3-030-35502-9_14
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DOI: https://doi.org/10.1007/978-3-030-35502-9_14
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