Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 62731, 11 pages
doi:10.1155/2007/62731
Research Article
Global Attractivity of Positive Periodic Solutions of Delay Differential Equations with Feedback Control
Department of Mathematics, School of Information Engineering, Lanzhou Commercial College, Lanzhou Gansu 730020, China
Received 8 August 2006; Accepted 26 November 2006
Copyright © 2007 Zhi-Long Jin. 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
By constructing suitable Liapunov functionals and estimating uniform upper
and lower bounds of solutions, sufficient conditions are obtained for the
global attractivity of positive periodic solutions of the delay differential
system with feedback control dy/dt=y(t)F(t,y(t−τ1(t)),…,y(t−τn(t)),u(t−δ(t))), du/dt=−η(t)u(t)+a(t)y(t−σ(t)). When these results are applied to the periodic logistic equation
with several delays and feedback control, some new results are obtained.