Oscillation and global attractivity in a discrete survival red blood cells model

I. Kubiaczyk, and S. H. Saker. "Oscillation and global attractivity in a discrete survival red blood cells model." Applicationes Mathematicae 30.4 (2003): 441-449. <http://eudml.org/doc/279208>.

@article{I2003,
abstract = {We consider the discrete survival red blood cells model (*) $N_\{n+1\} - Nₙ = -δₙNₙ + Pₙe^\{-aN_\{n-k\}\}$, where δₙ and Pₙ are positive sequences. In the autonomous case we show that (*) has a unique positive steady state N*, we establish some sufficient conditions for oscillation of all positive solutions about N*, and when k = 1 we give a sufficient condition for N* to be globally asymptotically stable. In the nonatonomous case, assuming that there exists a positive solution Nₙ*, we present necessary and sufficient conditions for oscillation of all positive solutions of (*) about Nₙ*. Our results can be considered as discrete analogues of the recent results by Saker and Agarwal [12] and solve an open problem posed by Kocic and Ladas [8].},
author = {I. Kubiaczyk, S. H. Saker},
journal = {Applicationes Mathematicae},
keywords = {oscillation; global attractivity; discrete survival red blood cells model; global asymptotic stability; positive solutions},
language = {eng},
number = {4},
pages = {441-449},
title = {Oscillation and global attractivity in a discrete survival red blood cells model},
url = {http://eudml.org/doc/279208},
volume = {30},
year = {2003},
}

TY - JOUR
AU - I. Kubiaczyk
AU - S. H. Saker
TI - Oscillation and global attractivity in a discrete survival red blood cells model
JO - Applicationes Mathematicae
PY - 2003
VL - 30
IS - 4
SP - 441
EP - 449
AB - We consider the discrete survival red blood cells model (*) $N_{n+1} - Nₙ = -δₙNₙ + Pₙe^{-aN_{n-k}}$, where δₙ and Pₙ are positive sequences. In the autonomous case we show that (*) has a unique positive steady state N*, we establish some sufficient conditions for oscillation of all positive solutions about N*, and when k = 1 we give a sufficient condition for N* to be globally asymptotically stable. In the nonatonomous case, assuming that there exists a positive solution Nₙ*, we present necessary and sufficient conditions for oscillation of all positive solutions of (*) about Nₙ*. Our results can be considered as discrete analogues of the recent results by Saker and Agarwal [12] and solve an open problem posed by Kocic and Ladas [8].
LA - eng
KW - oscillation; global attractivity; discrete survival red blood cells model; global asymptotic stability; positive solutions
UR - http://eudml.org/doc/279208
ER -