Bifurcation Phenomena. A Short Introductory Tutorial with Examples

Michiel Hazewinkel
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Michiel Hazewinkel: Erasmus University Rotterdam, Centre for Mathematics and Computer Science, Amsterdam amp; Econometric Institute

A chapter in Bifurcation Analysis, 1985, pp 13-30 from Springer

Abstract: 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.

Keywords: Equilibrium Point; HOPF Bifurcation; Bifurcation Diagram; Bifurcation Point; Equilibrium Price (search for similar items in EconPapers)
Date: 1985
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DOI: 10.1007/978-94-009-6239-2_2

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