title: Existence and exponential stability of positive almost periodic solution for Nicholson's blowflies models on time scales.
abstract: In this paper, we first give a new definition of almost periodic time scales, two new definitions of almost periodic functions on time scales and investigate some basic properties of them. Then, as an application, by using a fixed point theorem in Banach space and the time scale calculus theory, we obtain some sufficient conditions for the existence and exponential stability of positive almost periodic solutions for a class of Nicholson's blowflies models on time scales. Finally, we present an illustrative example to show the effectiveness of obtained results. Our results show that under a simple condition the continuous-time Nicholson's blowflies model and its discrete-time analogue have the same dynamical behaviors.
authors.affiliation: Department of Mathematics, Yunnan University, Kunming, 650091 Yunnan People's Republic of China.
authors.forename: Yongkun
authors.initials: Y
authors.lastname: Li
authors.affiliation: Department of Mathematics, Yunnan University, Kunming, 650091 Yunnan People's Republic of China.
authors.forename: Bing
authors.initials: B
authors.lastname: Li
keywords: Almost periodic solution; Almost periodic time scales; Exponential stability; Nicholsons blowflies model