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

Zhi-Long Jin

 Department of Mathematics, School of Information Engineering, Lanzhou Commercial College, Lanzhou Gansu 730020, China
Received 8 August 2006; Accepted 26 November 2006

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.