Existence of periodic and almost periodic solutions of discrete Ricker delay models. (English) Zbl 1318.39013

Hamaya, Yoshihiro

AlSharawi, Ziyad (ed.) et al., Theory and applications of difference equations and discrete dynamical systems. ICDEA, Muscat, Oman, May 26–30, 2013. Berlin: Springer (ISBN 978-3-662-44139-8/hbk; 978-3-662-44140-4/ebook). Springer Proceedings in Mathematics & Statistics 102, 171-185 (2014).

Summary: The aim of this article is to investigate sufficient conditions for the existence of periodic and almost periodic solutions of a generalized Ricker delay model, \[ N(n+1) = N(n)\exp \{f(n, N(n-r(n))) \}, \] when \(f\) are periodic and almost periodic functions in \(n \), respectively, which appears as a model for dynamics with single species in changing periodic and almost periodic environments, by applying the technique of boundedness and stability conditions which derives the fixed point theorems and uniformly asymptotically stable of solutions for above equation, respectively. Moreover, we consider the existence of an almost periodic solution of the case where \(f \) has the Volterra term with an infinite delay.
For the entire collection see [Zbl 1297.39001].

MSC:

39A23	Periodic solutions of difference equations
39A24	Almost periodic solutions of difference equations
39A12	Discrete version of topics in analysis
39A10	Additive difference equations
92D25	Population dynamics (general)

Keywords:

discrete Ricker delay models; population dynamics; periodic and almost periodic solutions; boundedness; stability