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Stabilizing a mathematical model of population system
Yan, Yubin Ekaka-A, Enu-Obari N.
Yan, Yubin
Ekaka-A, Enu-Obari N.
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2011-09-03
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Abstract
In this paper, we will consider how to stabilize a mathematical model, the Kolmogorov model, of the interactions of an n species population. The Lotka–Volterra model is a particular case of the more general Kolmogorov model. We first identify the unstable steady states of the model, then we use the feedback control based on the solutions of the Riccati equation to stabilize the linearized system. Finally we stabilize the nonlinear system by using the feedback controller obtained in the stabilization of the linearized system. We introduce the backward Euler method to approximate the feedback control nonlinear system and obtain the error estimates. Four numerical examples are given which come from the application areas.
Citation
Yan, Y. & Ekaka-a, Enu-Obari N. (2011). Stabilizing a mathematical model of population system. Journal of the Franklin Institute, 348(2011), 2744-2758. https://doi.org/10.1016/j.jfranklin.2011.08.014
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Elsevier
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Journal of the Franklin Institute
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DOI
10.1016/j.jfranklin.2011.08.014
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Article
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en
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0016-0032