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Bifurcation Phenomena. A Short Introductory Tutorial with Examples

In: Bifurcation Analysis

Author

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  • Michiel Hazewinkel

    (Erasmus University Rotterdam, Centre for Mathematics and Computer Science, Amsterdam amp; Econometric Institute)

Abstract

Many problems in the physical and the social sciences can be described (modelled) by equations or inequalities of one kind or another. E.g. simple polynomial equations such as x3-2x2 + 3x - 4 = 0 or a difference equation x(t+1)=2y(t)+x(t), y(t+1) = 2x(t)-y(t), or a differential equation ẋ(t) = - x2(t) + sin t, or much more complicated equations such as integro-differential equations, etcetera. In such a case a large part of solving the problem consists of solving the equation(s) and describing various properties of the nature of the solution (such as stability). Almost always such equations contain a number of parameters whose values are determined by the particular phenomenon being modelled. These are then usually not exactly known and may even change in time either in a natural way or because they are in the nature of control variables which can be adjusted to achieve certain goals.

Suggested Citation

  • Michiel Hazewinkel, 1985. "Bifurcation Phenomena. A Short Introductory Tutorial with Examples," Springer Books, in: M. Hazewinkel & R. Jurkovich & J. H. P. Paelinck (ed.), Bifurcation Analysis, pages 13-30, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-6239-2_2
    DOI: 10.1007/978-94-009-6239-2_2
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