We prove the existence and uniqueness of a positive periodic solution for a model describing the dynamics of cell volume flux, introduced by Julio A. Hernández [Bull. Math. Biol. 69 (2007), 1631-1648]. We also show that the periodic solution is a global attractor. Our results confirm the conjectures made in an interesting recent book of P. J. Torres [Atlantis Press, 2015].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap3857-3-2016,
author = {Philip Korman},
title = {A periodic model for the dynamics of cell volume},
journal = {Annales Polonici Mathematici},
volume = {116},
year = {2016},
pages = {243-249},
zbl = {06586885},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3857-3-2016}
}
Philip Korman. A periodic model for the dynamics of cell volume. Annales Polonici Mathematici, Tome 116 (2016) pp. 243-249. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3857-3-2016/