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Model-matching-based control of the Beverton-Holt equation in ecology. (English) Zbl 1149.92029
Summary: This paper discusses the generation of a carrying capacity of the environment so that the famous Beverton-Holt equation of ecology has a prescribed solution. The way used to achieve the tracking objective is the design of a carrying capacity through a feedback law so that the prescribed reference sequence, which defines the suitable behavior, is achieved. The advantage that the inverse of the Beverton-Holt equation is a linear time-varying discrete dynamic system whose external input is the inverse of the environment carrying capacity is taken in mind. In the case when the intrinsic growth rate is not perfectly known, an adaptive law implying parametrical estimation is incorporated into the scheme so that the tracking property of the reference sequence becomes an asymptotic objective in the absence of additive disturbances. The main advantage of the proposal is that the population evolution might behave as a prescribed one either for all time or asymptotically, which defines the desired population evolution. The technique might be of interest in some industrial exploitation problems like, for instance, in aquaculture management.

MSC:
92D40 Ecology
39A11 Stability of difference equations (MSC2000)
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[1] DOI: 10.1890/1051-0761(2003)013[0784:TVAPOC]2.0.CO;2
[2] DOI: 10.1016/S0165-7836(99)00126-5
[3] DOI: 10.1016/0165-7836(95)00377-M
[4] Fisheries Investment 19 pp 1– (1957)
[5] DOI: 10.1016/j.ecolmodel.2005.07.001
[6] DOI: 10.1016/S0304-3800(97)00104-X
[7] DOI: 10.1016/j.amc.2005.12.004 · Zbl 1100.93031
[8] DOI: 10.1155/DDNS/2006/37264 · Zbl 1149.39300
[9] DOI: 10.1016/S0096-3003(03)00291-1 · Zbl 1041.93029
[10] DOI: 10.1016/j.amc.2005.03.013 · Zbl 1111.93029
[11] DOI: 10.1155/DDNS/2006/41973
[12] DOI: 10.1109/9.788549 · Zbl 0957.93075
[13] DOI: 10.1016/j.amc.2005.11.004
[14] DOI: 10.1016/j.amc.2005.05.045 · Zbl 1086.92052
[15] DOI: 10.1016/j.amc.2005.12.024 · Zbl 1099.92069
[16] The Rocky Mountain Journal of Mathematics 37 (1) pp 79– (2007) · Zbl 1160.34071
[17] DOI: 10.1016/j.jmaa.2003.08.048 · Zbl 1046.34086
[18] DOI: 10.1155/2007/51406 · Zbl 1273.92015
[19] DOI: 10.1155/DDNS/2006/64590 · Zbl 1099.92071
[20] DOI: 10.1155/2007/48720 · Zbl 1179.92010
[21] Ecological Modelling 204 (1-2) pp 272– (2007)
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