International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 1, Pages 177-192
doi:10.1155/S0161171293000213

Feedback regulation of logistic growth

K. Gopalsamy1 and Pei-Xuan Weng1,2

1School of Infonmation Science and Technology, Flinders University, G.P.O. Box 2100, Adelaide 5001, Australia
2Department of Mathematics, South China Normal University, Guangzhou, China

Received 30 May 1991; Revised 20 November 1991

Copyright © 1993 K. Gopalsamy and Pei-Xuan Weng. 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

Sufficient conditions are obtained for the global asymptotic stability of the positive equilibrium of a regulated logistic growth with a delay in the state feedback of the control modelled by dn(t)dt=rn(t)[1−(a1n(t)+a2n(t−τ)K)−cu(t)]dn(t)dt=−au(t)+bn(t−τ) where u denotes an indirect control variable, r,a2,τ,a,b,c∈(0,∞) and a1∈[0,∞).