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Instabilities and chaos in nonlinear dynamic systems
Author(s) -
Mosekilde Erik,
Aracil Javier,
Allen Peter M.
Publication year - 1988
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.4260040104
Subject(s) - nonlinear system , chaos (operating system) , chaos theory , computer science , statistical physics , instability , stability (learning theory) , field (mathematics) , control theory (sociology) , mathematics , physics , chaotic , artificial intelligence , mechanics , computer security , control (management) , quantum mechanics , machine learning , pure mathematics
Increasing computational power in the last decade has led to a breakthrough in the understanding of nonlinear dynamic systems. Deterministic chaos, a distinct mode of behavior qualitatively different from linear modes, can arise in systems with instabilities constrained by nonlinearities. This article overviews this new field. It is observed that deterministic chaos is associated with the presence of a basic instability, often associated with a negative loop with high‐gain and significant delay, that allows small random fluctuations to be amplified and eventually dominate the behavior of the system. The mathematical tools of qualitative analysis of nonlinear systems are applied to familiar models of urban dynamics. Spatial disaggregation in an urban migration model is shown to yield a route to chaos through period‐doubling. Alternative routes to chaos are discussed. Examples from the natural and social sciences are used to demonstrate the applicability of the tools and the ubiquity of such complex nonlinear dynamic phenomena.