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@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, vol.~75, No~5, p.~1235-1251. ISSN~0303-6812. doi:10.1007/s00285-017-1115-8. 2017.
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