Two parametric bifurcations in LPA model

J 2017

Two parametric bifurcations in LPA model

HAJNOVÁ, Veronika a Lenka PŘIBYLOVÁ

Základní údaje

Originální název

Two parametric bifurcations in LPA model

Název česky

Dvouparametrické bifurkace v LPA modelu

Autoři

HAJNOVÁ, Veronika (203 Česká republika, domácí) a Lenka PŘIBYLOVÁ (203 Česká republika, garant, domácí)

Vydání

Journal of Mathematical Biology, HEIDELBERG, SPRINGER HEIDELBERG, 2017, 0303-6812

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Německo

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.786

Kód RIV

RIV/00216224:14310/17:00096295

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1007/s00285-017-1115-8

UT WoS

000409891600007

Klíčová slova česky

Populační dynamika; dvouparametrické bifurkace; LPA model; Silná 1:2 rezonance; Chencinerova bifurkace

Klíčová slova anglicky

Population dynamics; Two-parameter bifurcations; LPA model; Strong 1:2 resonance; Chenciner bifurcation

Štítky

NZ, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 12. 4. 2018 17:11, Ing. Nicole Zrilić

Anotace

V originále

The structured population LPA model is studied. The model describes flour beetle (Tribolium) population dynamics of four stage populations: eggs, larvae, pupae and adults with cannibalism between these stages. We concentrate on the case of non-zero cannibalistic rates of adults on eggs and adults on pupae and no cannibalism of larvae on eggs, but the results can be numerically continued to non-zero cannibalism of larvae on eggs. In this article two-parameter bifurcations in LPA model are analysed. Various stable and unstable invariant sets are found, different types of hysteresis are presented and abrupt changes in dynamics are simulated to explain the complicated way the system behaves near two-parameter bifurcation manifolds. The connections between strong 1:2 resonance and Chenciner bifurcations are presented as well as their very significant consequences to the dynamics of the Tribolium population. The hysteresis phenomena described is a generic phenomenon nearby the Chenciner bifurcation or the cusp bifurcation of the loop.

Návaznosti

MUNI/A/1234/2015, interní kód MU

Název: Matematické a statistické modelování (Akronym: Matematické a statistické modelování)

Investor: Masarykova univerzita, Matematické a statistické modelování, DO R. 2020_Kategorie A - Specifický výzkum - Studentské výzkumné projekty

Citovat

HAJNOVÁ, Veronika a Lenka PŘIBYLOVÁ. Two parametric bifurcations in LPA model. Journal of Mathematical Biology. HEIDELBERG: SPRINGER HEIDELBERG, 2017, roč. 75, č. 5, s. 1235-1251. ISSN 0303-6812. Dostupné z: https://dx.doi.org/10.1007/s00285-017-1115-8.

@article{1375585,
   author = {Hajnová, Veronika and Přibylová, Lenka},
   article_location = {HEIDELBERG},
   article_number = {5},
   doi = {http://dx.doi.org/10.1007/s00285-017-1115-8},
   keywords = {Population dynamics; Two-parameter bifurcations; LPA model; Strong 1:2 resonance; Chenciner bifurcation},
   language = {eng},
   issn = {0303-6812},
   journal = {Journal of Mathematical Biology},
   title = {Two parametric bifurcations in LPA model},
   url = {http://link.springer.com/article/10.1007%2Fs00285-017-1115-8},
   volume = {75},
   year = {2017}
}

TY  - JOUR
ID  - 1375585
AU  - Hajnová, Veronika - Přibylová, Lenka
PY  - 2017
TI  - Two parametric bifurcations in LPA model
JF  - Journal of Mathematical Biology
VL  - 75
IS  - 5
SP  - 1235-1251
EP  - 1235-1251
PB  - SPRINGER HEIDELBERG
SN  - 03036812
KW  - Population dynamics
KW  - Two-parameter bifurcations
KW  - LPA model
KW  - Strong 1:2 resonance
KW  - Chenciner bifurcation
UR  - http://link.springer.com/article/10.1007%2Fs00285-017-1115-8
L2  - http://link.springer.com/article/10.1007%2Fs00285-017-1115-8
N2  - The structured population LPA model is studied. The model describes flour beetle (Tribolium) population dynamics of four stage populations: eggs, larvae, pupae and adults with cannibalism between these stages. We concentrate on the case of non-zero cannibalistic rates of adults on eggs and adults on pupae and no cannibalism of larvae on eggs, but the results can be numerically continued to non-zero cannibalism of larvae on eggs. In this article two-parameter bifurcations in LPA model are analysed. Various stable and unstable invariant sets are found, different types of hysteresis are presented and abrupt changes in dynamics are simulated to explain the complicated way the system behaves near two-parameter bifurcation manifolds. The connections between strong 1:2 resonance and Chenciner bifurcations are presented as well as their very significant consequences to the dynamics of the Tribolium population. The hysteresis phenomena described is a generic phenomenon nearby the Chenciner bifurcation or the cusp bifurcation of the loop.
ER  -

HAJNOVÁ, Veronika a Lenka PŘIBYLOVÁ. Two parametric bifurcations in LPA model. \textit{Journal of Mathematical Biology}. HEIDELBERG: SPRINGER HEIDELBERG, 2017, roč.~75, č.~5, s.~1235-1251. ISSN~0303-6812. Dostupné z: https://dx.doi.org/10.1007/s00285-017-1115-8.

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