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Structural Stability

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Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 250)

Abstract

In every mathematical investigation, the question will arise whether we can apply our mathematical results to the real world. Indeed, let us assume that the result is very sensitive to the smallest change in the model. In such a case, an arbitrarily small change in the model (say, a small change of the vector field defining a differential equation) leads to another model with essentially different properties. A result like this cannot be transferred to the real process under consideration, because, when constructing the model, the real situation was idealized and simplified, the parameters were determined only approximately, etc. Consequently, the question arises of choosing those properties of the model of a process which are not very sensitive to small changes in the model, and thus may be viewed as properties of the real process.

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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteMoscow GSP-1USSR

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