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

Xianhua Tang; Xingfu Zou

doi:10.3934/dcdsb.2002.2.265

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2002, Volume 2, Issue 2: 265-278. Doi: 10.3934/dcdsb.2002.2.265

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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
2.
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF, A1C5S7

Received: May 2001

Revised: October 2001

Published: May 2002

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Abstract

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.

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Mathematics Subject Classification: 34K11, 34K20.

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