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Bifurcation and Pattern Formation in an Activator–Inhibitor Model with Non-local Dispersal.
- Source :
-
Bulletin of Mathematical Biology . Dec2022, Vol. 84 Issue 12, p1-31. 31p. - Publication Year :
- 2022
-
Abstract
- In this paper, by approximating the non-local spatial dispersal equation by an associated reaction–diffusion system, an activator–inhibitor model with non-local dispersal is transformed into a reaction–diffusion system coupled with one ordinary differential equation. We prove that, to some extent, the non-locality-induced instability of the non-local system can be regarded as diffusion-driven instability of the reaction–diffusion system for sufficiently small perturbation. We study the structure of the spectrum of the corresponding linearized operator, and we use linear stability analysis and steady-state bifurcations to show the existence of non-constant steady states which generates non-homogeneous spatial patterns. As an example of our results, we study the bifurcation and pattern formation of a modified Klausmeier–Gray–Scott model of water–plant interaction. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00928240
- Volume :
- 84
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Bulletin of Mathematical Biology
- Publication Type :
- Academic Journal
- Accession number :
- 159968240
- Full Text :
- https://doi.org/10.1007/s11538-022-01098-0