Bifurcations in Nagumo Equations on Graphs and Fiedler Vectors

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F23%3A43969128" target="_blank" >RIV/49777513:23520/23:43969128 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s10884-021-10101-6" target="_blank" >https://link.springer.com/article/10.1007/s10884-021-10101-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10884-021-10101-6" target="_blank" >10.1007/s10884-021-10101-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Bifurcations in Nagumo Equations on Graphs and Fiedler Vectors

Popis výsledku v původním jazyce

Reaction-diffusion equations serve as a basic framework for numerous dynamic phenomena like pattern formation and travelling waves. Spatially discrete analogues of Nagumo reaction-diffusion equation on lattices and graphs provide insights how these phenomena are strongly influenced by the discrete and continuous spatial structures. Specifically, Nagumo equations on graphs represent rich high dimensional problems which have an exponential number of stationary solutions in the case when the reaction dominates the diffusion. In contrast, for sufficiently strong diffusion there are only three constant stationary solutions. We show that the emergence of the spatially heterogeneous solutions is closely connected to the second eigenvalue of the Laplacian matrix of a graph, the algebraic connectivity. For graphs with simple algebraic connectivity, the exact type of bifurcation of these solutions is implied by the properties of the corresponding eigenvector, the so-called Fiedler vector.

Název v anglickém jazyce

Bifurcations in Nagumo Equations on Graphs and Fiedler Vectors

Popis výsledku anglicky

Reaction-diffusion equations serve as a basic framework for numerous dynamic phenomena like pattern formation and travelling waves. Spatially discrete analogues of Nagumo reaction-diffusion equation on lattices and graphs provide insights how these phenomena are strongly influenced by the discrete and continuous spatial structures. Specifically, Nagumo equations on graphs represent rich high dimensional problems which have an exponential number of stationary solutions in the case when the reaction dominates the diffusion. In contrast, for sufficiently strong diffusion there are only three constant stationary solutions. We show that the emergence of the spatially heterogeneous solutions is closely connected to the second eigenvalue of the Laplacian matrix of a graph, the algebraic connectivity. For graphs with simple algebraic connectivity, the exact type of bifurcation of these solutions is implied by the properties of the corresponding eigenvector, the so-called Fiedler vector.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Dynamics and Differential Equations

ISSN

1040-7294

e-ISSN

1572-9222

Svazek periodika

35

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

16

Strana od-do

2397-2412

Kód UT WoS článku

000713551100001

EID výsledku v databázi Scopus

2-s2.0-85118355134