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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 798961, 9 pages
http://dx.doi.org/10.1155/2013/798961
Research Article

Permanence, Extinction, and Almost Periodic Solution of a Nicholson's Blowflies Model with Feedback Control and Time Delay

Sunshine College, Fuzhou University, Fuzhou, Fujian 350015, China

Received 20 February 2013; Accepted 7 April 2013

Academic Editor: Yonghui Xia

Copyright © 2013 Haihui Wu and Shengbin Yu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A Nicholson's blowflies model with feedback control and time delay is studied. By applying the comparison theorem of the differential equation and fluctuation lemma and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence, extinction, and existence of a unique globally attractive positive almost periodic solution of the system are obtained. It is proved that the feedback control variable and time delay have no influence on the permanence and extinction of the system.