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Remarks on an environmental control problem. (English) Zbl 0924.92025

Horn, Mary Ann (ed.) et al., Mathematical models in medical and health science. International conference, Vanderbilt University, Nashville, TN, USA, May 28–31, 1997. La Vergne, TN: Vanderbilt University Press. Innovations in Applied Mathematics. 267-279 (1998).
Summary: The model of D. M. Thomas et al. [Math. Biosci. 133, No. 2, 139-163 (1996; Zbl 0844.92026)] for zoo-plankton/pollutant interaction in a fresh water environment is considered with a modified pollutant input function. General conditions are presented under which a relaxed feed-back control of the pollutant input drives the dynamics of the model to a steady state where the environmental pollutant concentration is below a prescribed threshold. Complementarily, a scenario is described where the system converges towards a periodic orbit for almost all initial conditions.
For the entire collection see [Zbl 0910.00060].

MSC:

92D40 Ecology
93C95 Application models in control theory
49N70 Differential games and control
49N75 Pursuit and evasion games
93C15 Control/observation systems governed by ordinary differential equations

Citations:

Zbl 0844.92026
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