On a generalization of the global attractivity for a periodically forced Pielou's equation

TL;DR

This paper investigates the global attractivity of a generalized periodically forced Pielou's difference equation, characterizing its long-term behavior and extending previous results with new conditions and examples.

Contribution

It generalizes recent findings on the global dynamics of periodically forced Pielou's equations, providing broader conditions for stability and attractivity.

Findings

Zero solution is globally attractive under certain conditions

Existence of a globally attractive periodic solution in some cases

Provides examples illustrating the theoretical results

Abstract

In this paper, we study the global attractivity for a class of periodic difference equation with delay which has a generalized form of Pielou's difference equation. The global dynamics of the equation is characterized by using a relation between the upper and lower limit of the solution. There are two possible global dynamics: zero solution is globally attractive or there exists a periodic solution which is globally attractive. Recent results in [E. Camouzis, G. Ladas, Periodically forced Pielou's equation, J. Math. Anal. Appl. 333 (1) (2007) 117-127] is generalized. Two examples are given to illustrate our results.