Differential Equation Modeling as a Source of Theoretical Insight: Four Disparate Examples

Differential Equation Modeling as a Source of Theoretical Insight: Four Disparate Examples We explore differential equations involving alcoholism, socialmobility, excess female mortality, and international arms competition.In each of these instances we show that the initial equation, orsystem of equations, has a sociological plausibility comparable tothat of the associated solutions; the solutions do indeed describetime-series trajectories that seem to represent important and uniquesocial processes. We argue that the central challenge of differentialequation modeling is to use experimentation to clarifyrelationships between, on the one hand, the equations andtheir coefficients and, on the other, the solutions and thetime-series orbits created by them. Such feedback interaction ofdifferential equations and their solutions appears to be the basis forfurther theoretical insight, and rapid assessments of theseinteractions are now possible largely because modern softwareencourages experimentation with many combinations of inputcoefficients. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

Differential Equation Modeling as a Source of Theoretical Insight: Four Disparate Examples

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Publisher
Springer Journals
Copyright
Copyright © 2002 by Kluwer Academic Publishers
Subject
Social Sciences; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1023/A:1014976416218
Publisher site
See Article on Publisher Site

Abstract

We explore differential equations involving alcoholism, socialmobility, excess female mortality, and international arms competition.In each of these instances we show that the initial equation, orsystem of equations, has a sociological plausibility comparable tothat of the associated solutions; the solutions do indeed describetime-series trajectories that seem to represent important and uniquesocial processes. We argue that the central challenge of differentialequation modeling is to use experimentation to clarifyrelationships between, on the one hand, the equations andtheir coefficients and, on the other, the solutions and thetime-series orbits created by them. Such feedback interaction ofdifferential equations and their solutions appears to be the basis forfurther theoretical insight, and rapid assessments of theseinteractions are now possible largely because modern softwareencourages experimentation with many combinations of inputcoefficients.

Journal

Quality & QuantitySpringer Journals

Published: Oct 13, 2004

References

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