Bifurcations in Nagumo Equations on Graphs and Fiedler Vectors
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Bifurcations in Nagumo Equations on Graphs and Fiedler Vectors
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Dynamics and Differential Equations
ISSN
1040-7294
e-ISSN
1572-9222
Volume of the periodical
35
Issue of the periodical within the volume
3
Country of publishing house
GB - UNITED KINGDOM
Number of pages
16
Pages from-to
2397-2412
UT code for WoS article
000713551100001
EID of the result in the Scopus database
2-s2.0-85118355134