Bifurcation and pattern formation in diffusive Klausmeier-Gray-Scott model of water-plant interaction

Autor:	Junping Shi, Guohong Zhang, Xiaoli Wang
Rok vydání:	2021
Předmět:	Applied Mathematics 010102 general mathematics Pattern formation Water plant 01 natural sciences Shadow system Physics::Geophysics 010101 applied mathematics Patterned vegetation Amplitude Homogeneous Statistical physics 0101 mathematics Analysis Bifurcation methods Bifurcation Mathematics
Zdroj:	Journal of Mathematical Analysis and Applications. 497:124860
ISSN:	0022-247X
DOI:	10.1016/j.jmaa.2020.124860
Popis:	A reaction-diffusion model describing water and plant interaction proposed by Klausmeier is studied. The existence of non-constant steady state solutions is shown through bifurcation methods, and the existence of large amplitude spatial patterned solutions is proved using associated shadow system. It is rigorously shown that non-homogeneous patterned vegetation states exist when the rainfall is at a lower level in which homogeneous vegetation state cannot survive. Even when the rainfall is very low, slow plant diffusion and fast water diffusion can support a vegetation state with vegetation concentrating on a small area. This provides an example of diffusion-induced persistence that non-constant steady states may exist in a reaction-diffusion system when there are no positive constant steady states.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::527b994bf05d991184d17f17c85aed8b https://doi.org/10.1016/j.jmaa.2020.124860 Zobrazit plný text záznamu Full Text from ScienceDirect