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2003, Volume 2003: 359-364. Doi: 10.3934/proc.2003.2003.359 open access
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A nonlinear controlled system of differential equations describing the process of production and sales of a consumer good

  • 1.

    Department of Mathematics and Computer Sciences, Texas Woman's University, Denton, TX 76204

  • 2.

    Department of Computer Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, 119992

Received:  June 30, 2002
Published:  March 2003
Abstract Related Papers Cited by
    Abstract
  • A nonlinear controlled system of differential equations has been constructed to describe the process of production and sales of a consumer good. This model can be controlled either by the rate of production or by the price of the good. The attainable sets of corresponding controlled systems are studied. It is shown that in both cases the boundaries of these sets are the unions of two two-parameter surfaces. It is proved that every point on the boundaries of the attainable sets is a result of piecewise constant controls with at most two switchings. Attainable sets for different values of parameters of the model will be demonstrated using MAPLE.
    Mathematics Subject Classification: 49J15, 58E25, 90A16, 93B03.

    Citation:
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