Nonuniqueness of implicit lattice Nagumo equation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F19%3A43954902" target="_blank" >RIV/49777513:23520/19:43954902 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.21136/AM.2019.0270-18" target="_blank" >https://doi.org/10.21136/AM.2019.0270-18</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/AM.2019.0270-18" target="_blank" >10.21136/AM.2019.0270-18</a>

Result language
angličtina
Original language name
Nonuniqueness of implicit lattice Nagumo equation
Original language description
We consider the implicit discretization of Nagumo equation on finite lattices and show that its variational formulation corresponds in various parameter settings to convex, mountain-pass or saddle-point geometries. Consequently, we are able to derive conditions under which the implicit discretization yields multiple solutions. Interestingly, for certain parameters we show nonuniqueness for arbitrarily small discretization steps. Finally, we provide a simple example showing that the nonuniqueness can lead to complex dynamics in which the number of bounded solutions grows exponentially in time iterations, which in turn implies infinite number of global trajectories.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/LO1506" target="_blank" >LO1506: Sustainability support of the centre NTIS - New Technologies for the Information Society</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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