J
2019
Bifurcation manifolds in predator–prey models computed by Gröbner basis method
HAJNOVÁ, Veronika and Lenka PŘIBYLOVÁ
Basic information
Original name
Bifurcation manifolds in predator–prey models computed by Gröbner basis method
Name in Czech
Bifurkační variety v modelech predátor-kořist vypočítané pomocí Gröbnerových bazí
Edition
Mathematical Biosciences, Amsterdam, Elsevier, 2019, 0025-5564
Other information
Type of outcome
Článek v odborném periodiku
Field of Study
10102 Applied mathematics
Country of publisher
United States of America
Confidentiality degree
není předmětem státního či obchodního tajemství
Impact factor
Impact factor: 1.649
RIV identification code
RIV/00216224:14310/19:00109406
Organization unit
Faculty of Science
Keywords (in Czech)
Rosenzweigův–MacArthurův model; Bifurkační variety; Gröbnerovy báze; Hopfova bifurkace; Fold bifurkace; Model predátor-kořist
Keywords in English
Rosenzweig–MacArthur model; Bifurcation manifolds; Gröbner basis; Hopf bifurcation; Fold bifurcation; Predator–prey model
Tags
International impact, Reviewed
V originále
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.
Links
MUNI/A/1204/2017, interní kód MU | Name: Matematické statistické modelování 2 (Acronym: MaStaMo2) | Investor: Masaryk University, Category A |
|
MUNI/A/1503/2018, interní kód MU | Name: Matematické statistické modelování 3 (Acronym: MaStaMo3) | Investor: Masaryk University, Category A |
|
Displayed: 5/12/2024 05:57