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Complex dynamics in low‐dimensional continuous‐time business cycle models: The Šil nikov case
Author(s) -
Lorenz HansWalter
Publication year - 1992
Publication title -
system dynamics review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 57
eISSN - 1099-1727
pISSN - 0883-7066
DOI - 10.1002/sdr.4260080304
Subject(s) - chaotic , business cycle , nonlinear system , homoclinic orbit , simple (philosophy) , dynamics (music) , multiplier (economics) , complex dynamics , mathematical economics , motion (physics) , computer science , mathematics , economics , mathematical analysis , keynesian economics , artificial intelligence , physics , bifurcation , philosophy , quantum mechanics , acoustics , epistemology
While most examples of complex motion in economic dynamics employ a discrete‐time concept, chaos can also emerge in continuous‐time, nonlinear economic models. It is argued that, (depending on the level of aggregation in the economy) the use of the continuous‐time concept can be mandatory in economic dynamics. The Šil'nikov scenario, based on the existence of homoclinic orbits, is used as a formal means to illustrate the emergence of complex motion in two simple examples from traditional business cycle theory. The consideration of slight nonlinearities in a generalized version of the standard Metzler model with inventories and in Phillips' multiplier‐accelerator model can imply chaotic behavior.