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

• Autorzy: I. Kubiaczyk , S. H. Saker
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 39A10: Difference equations, additive
• 92D25: Population dynamics (general)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2003
• Tom: 30
• Numer: 4
• Strony: 441-449

Daty

wydano

2003

Twórcy

autor

I. Kubiaczyk

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

autor

S. H. Saker

• Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

Identyfikatory

DOI

10.4064/am30-4-6