Two parametric bifurcations in LPA model

J 2017

Two parametric bifurcations in LPA model

HAJNOVÁ, Veronika and Lenka PŘIBYLOVÁ

Basic information

Original name

Two parametric bifurcations in LPA model

Name in Czech

Dvouparametrické bifurkace v LPA modelu

Authors

HAJNOVÁ, Veronika (203 Czech Republic, belonging to the institution) and Lenka PŘIBYLOVÁ (203 Czech Republic, guarantor, belonging to the institution)

Edition

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

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 1.786

RIV identification code

RIV/00216224:14310/17:00096295

Organization unit

Faculty of Science

DOI

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

UT WoS

000409891600007

Keywords (in Czech)

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

Keywords in English

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

Abstract

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.

Links

MUNI/A/1234/2015, interní kód MU

Name: Matematické a statistické modelování (Acronym: Matematické a statistické modelování)

Investor: Masaryk University, Category A

Citovat

HAJNOVÁ, Veronika and Lenka PŘIBYLOVÁ. Two parametric bifurcations in LPA model. Journal of Mathematical Biology. HEIDELBERG: SPRINGER HEIDELBERG, 2017, vol. 75, No 5, p. 1235-1251. ISSN 0303-6812. Available from: 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 and Lenka PŘIBYLOVÁ. Two parametric bifurcations in LPA model. \textit{Journal of Mathematical Biology}. HEIDELBERG: SPRINGER HEIDELBERG, 2017, vol.~75, No~5, p.~1235-1251. ISSN~0303-6812. Available from: https://dx.doi.org/10.1007/s00285-017-1115-8.

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