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May  2002, 2(2): 265-278. doi: 10.3934/dcdsb.2002.2.265

A 3/2 stability result for a regulated logistic growth model

Xianhua Tang 1, and  Xingfu Zou 2,

1. 

Department of Applied Mathematics, Central South University, Changsha, Hunan 410083, China
2. 

Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF, A1C5S7

Received  May 2001 Revised  October 2001 Published  February 2002

A sufficient condition is established for globally asymptotic stability of the positive equilibrium of a regulated logistic growth model with a delay in the state feedback. The result improves some existing criteria for this model. It is in a form that is related to the number $3/2$ and the coupling strength, and thus, is comparable to the well-known $3/2$ condition for the uncontrolled delayed logistic equation. The comparison seems to suggest that the mechanism of the control in this model might be inappropriate and new mechanism should be introduced.
Keywords: Logistic, feedback regulation., global stability.
Mathematics Subject Classification: 34K11, 34K2.
Citation: Xianhua Tang, Xingfu Zou. A 3/2 stability result for a regulated logistic growth model. Discrete and Continuous Dynamical Systems - B, 2002, 2 (2) : 265-278. doi: 10.3934/dcdsb.2002.2.265
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