| Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Growth phenomena
|
|
|---|---|---|
| Article Number | 4 | |
| Number of page(s) | 12 | |
| DOI | https://doi.org/10.1051/mmnp/2019046 | |
| Published online | 14 February 2020 | |
On the shape of invading population in anisotropic environments
Department for Computer Simulations of Many-Particle Systems, Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine,
Lviv
79011, Ukraine.
* Corresponding author: blavatskav@gmail.com
Received:
22
May
2019
Accepted:
19
October
2019
We analyze the properties of population spreading in environments with spatial anisotropy within the frames of a lattice model of asymmetric (biased) random walkers. The expressions for the universal shape characteristics of the instantaneous configuration of population, such as asphericity A and prolateness S are found analytically and proved to be dependent only on the asymmetric transition probabilities in different directions. The model under consideration is shown to capture, in particular, the peculiarities of invasion in presence of an array of oriented tubes (fibers) in the environment.
Mathematics Subject Classification: 60G50 / 62P10 / 65C60
Key words: Random walk / heterogeneous environment / biological invasion
© EDP Sciences, 2020
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