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Education and Development BIFURCATIONS IN DYNAMICAL SYSTEMS
Author(s) -
Majthay Antal
Publication year - 1980
Publication title -
decision sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.238
H-Index - 108
eISSN - 1540-5915
pISSN - 0011-7315
DOI - 10.1111/j.1540-5915.1980.tb01146.x
Subject(s) - catastrophe theory , dynamical systems theory , mathematical economics , bifurcation , dynamical system (definition) , bifurcation theory , statistical physics , computer science , mathematics , physics , nonlinear system , geotechnical engineering , quantum mechanics , engineering
The concept of bifurcation in a dynamical system is illustrated through several examples. The elementary catastrophes are equilibrium sets of specific kinds of dynamical systems. The framework of bifurcating dynamical systems is put forward as an alternative to catastrophe theory models. Dynamical systems models require explicit accounting of all their underlying hypotheses. They offer unambiguous answers in return. The fuzzy transition from hypotheses to results so characteristic of the catastrophe theory literature is absent. The method is illustrated using a stock‐market model.