Stability analysis of Pielou's equation with period-two coefficient
Document Type
Article
Date of Original Version
5-1-2007
Abstract
We study global attractivity of the period-two coefficient version of the delay logistic difference equation, also known as Pielou's equation,[image omitted]where[image omitted]We prove that for [image omitted], zero is the unique equilibrium point. If [image omitted], then zero is globally asymptotically stable, with basin of attraction given by the nonnegative quadrant of initial conditions. If [image omitted], then zero is unstable, and a sequence [image omitted] converges to zero if and only if [image omitted]. If [image omitted], then the sequence [image omitted] converges to the unique period-two solution[image omitted]where [image omitted] and [image omitted] are uniquely determined by the equations[image omitted].
Publication Title, e.g., Journal
Journal of Difference Equations and Applications
Volume
13
Issue
5
Citation/Publisher Attribution
Kulenović, M. R., and Orlando Merino. "Stability analysis of Pielou's equation with period-two coefficient." Journal of Difference Equations and Applications 13, 5 (2007): 383-406. doi: 10.1080/10236190601045929.
