Bifurcation manifolds in predator–prey models computed by Gröbner basis method
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F19%3A00109406" target="_blank" >RIV/00216224:14310/19:00109406 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.mbs.2019.03.008" target="_blank" >https://doi.org/10.1016/j.mbs.2019.03.008</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.mbs.2019.03.008" target="_blank" >10.1016/j.mbs.2019.03.008</a>
Alternative languages
Result language
angličtina
Original language name
Bifurcation manifolds in predator–prey models computed by Gröbner basis method
Original language description
Many natural processes studied in population biology, systems biology, biochemistry, chemistry or physics are modeled by dynamical systems with polynomial or rational right-hand sides in state and parameter variables. The problem of finding bifurcation manifolds of such discrete or continuous dynamical systems leads to a problem of finding solutions to a system of non-linear algebraic equations. This approach often fails since it is not possible to express equilibria explicitly. Here we describe an algebraic procedure based on the Gröbner basis computation that finds bifurcation manifolds without computing equilibria. Our method provides formulas for bifurcation manifolds in commonly studied cases in applied research – for the fold, transcritical, cusp, Hopf and Bogdanov–Takens bifurcations. The method returns bifurcation manifolds as implicitly defined functions or parametric functions in full parameter space. The approach can be implemented in any computer algebra system; therefore it can be used in applied research as a supporting autonomous computation even by non-experts in bifurcation theory. This paper demonstrates our new approach on the recently published Rosenzweig–MacArthur predator–prey model generalizations in order to highlight the simplicity of our method compared to the published analysis.
Czech name
—
Czech description
—
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
10102 - Applied mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Biosciences
ISSN
0025-5564
e-ISSN
1879-3134
Volume of the periodical
312
Issue of the periodical within the volume
JUN 2019
Country of publishing house
US - UNITED STATES
Number of pages
7
Pages from-to
1-7
UT code for WoS article
000469895200001
EID of the result in the Scopus database
2-s2.0-85063868259