Li Y, Li B. Existence and exponential stability of positive almost periodic solution for Nicholson's blowflies models on time scales.
SPRINGERPLUS 2016;
5:1096. [PMID:
27468397 PMCID:
PMC4947086 DOI:
10.1186/s40064-016-2700-9]
[Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/19/2016] [Accepted: 06/28/2016] [Indexed: 12/03/2022]
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.
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