A Lyapunov function for piecewise-independent differential equations: stability of the ideal free distribution in two patch environments
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60077344%3A_____%2F07%3A00080591" target="_blank" >RIV/60077344:_____/07:00080591 - isvavai.cz</a>
Alternative codes found
RIV/60076658:12310/07:00007984
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
A Lyapunov function for piecewise-independent differential equations: stability of the ideal free distribution in two patch environments
Original language description
In this article we construct Lyapunov functions formodels described by piecewise-continuous and independent differential equations. Because these models are described by discontinuous differential equations, the theory of Lyapunov functions for smooth dynamical systems is not applicable. Instead, we use a geometrical approach to construct a Lyapunov function. Then we apply the general approach to analyze population dynamics describing exploitative competition of two species in a two-patch environment. We prove that for any biologically meaningful parameter combination the model has a globally stable equilibrium and we analyze this equilibrium with respect to parameters.
Czech name
Lypunovova funkce pro modely popsané po částech nezávislými diferenciálními rovnicemi: Stabilita prostorového rozložení populací
Czech description
Práce se zabývá stabilitou modelů popsaných po částech nezávislými diferenciálními rovnicemi. Takové modely se vyskytují při popisu genových sítí, v ekologii a pod. Teoretické výsledky jsou v práci aplikovány na model populační dynamiky dvou kompetujících si druhů.
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/IAA100070601" target="_blank" >IAA100070601: Mathematical models of biological networks</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2007
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 Mathematical Biology
ISSN
0303-6812
e-ISSN
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Volume of the periodical
54
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
24
Pages from-to
465-488
UT code for WoS article
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EID of the result in the Scopus database
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