Discrete Reaction-Dispersion Equation
| Authors | |
|---|---|
| Year of publication | 2020 |
| Type | Article in Proceedings |
| Conference | Difference Equations and Discrete Dynamical Systems with Applications |
| MU Faculty or unit | |
| 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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