Titlebook: Attractors, Bifurcations, and Chaos; Nonlinear Phenomena Tönu Puu Book 20001st edition Springer-Verlag Berlin Heidelberg 2000 bifurcation.

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Introduction,Dynamic analysis in economics is as old as economics itself. A glance at the subject index in Joseph Schumpeter’s monumental . is sufficient to convince you about this. Even dynamic mathematical models are fairly old. Cournot duopoly dates back to 1838 and the cobweb model of price adjustments to 1887.

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Iterated Maps or Difference Equations,In Chapter 2 we saw that the behaviour of differential equations could be studied in terms of first return maps for points on the Poincaré section to itself. In this way the maps are related to differential equation systems.

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Bifurcation and Catastrophe,On several occasions we already encountered the concept of bifurcation. In Sections 2.5–2.6 we for instance discussed the Hopf bifurcation from fixed point to limit cycle, and the saddle-node bifurcation, which again broke up the continuous cycle into a discrete set of fixed points.

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Duopoly and Oligopoly,Economics recognizes two opposite market forms: competition and monopoly. In the competitive case the firms are very numerous and thus small in relation to the total size of the market. In consequence they consider market price as being approximately given independently of any action they can take on their own with regard to their supply.

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