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A nonlinear controlled system of differential equations describing the process of production and sales of a consumer good

Pages: 359 - 364, Issue Special, July 2003

 Abstract        Full Text (269.7K)              

Ellina Grigorieva - Department of Mathematics and Computer Sciences, Texas Woman's University, Denton, TX 76204, United States (email)
Evgenii Khailov - Department of Computer Mathematics and Cybernetics, Moscow State Lomonosov University, Moscow, 119992, Russian Federation (email)

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.

Keywords:  Nonlinear controlled system, attainable set, microeconomic dynamical model.
Mathematics Subject Classification:  49J15, 58E25, 90A16, 93B03.

Received: July 2002; Published: April 2003.