Dynamic Modeling: An Introduction

by R . Robert Huckfeldt, Carol W. Kohfeld, Thomas W. Likens

Overview

This short monograph lays out the theory behind, and techniques for, using dynamic modelling, taking the reader through a series of increasingly complex models. At each step, examples are used to explain the process, and also to clarify specific applications of difference equation models in the social sciences.

'It is a good example of classical mathematical model building and I may well use it as a text for the course on that subject in our MSc on Quantitative Methods in the Behavioural Sciences...in general it is to be recommended.' — Bethlem and Maudsley Gazette, Vol 31 No 2, 1983

Product Details

ISBN-13:	9780803909465
Publisher:	SAGE Publications
Publication date:	10/01/1982
Series:	Quantitative Applications in the Social Sciences , #27
Edition description:	New Edition
Pages:	95
Product dimensions:	5.50(w) x 8.50(h) x 0.24(d)

Table of Contents

	Series Editor's Introduction	5
	Acknowledgments	6
1.	Dynamic Models and Social Change	7
	Difference Equations as Representations of Change	7
	Synchronic versus Diachronic Change	9
	Dynamic Models and Other Models of Change	9
	The Structure of the Presentation	10
2.	First-Order Linear Difference Equation Models: A Model of the Mobilization Process	10
	A First Dynamic Model: The Gain/Loss Formulation	11
	Difference Equations as Representative of Change	14
	Solutions to First-Order Difference Equations	15
	Equilibrium and Stability	17
	Substantive Applications	20
	Model Estimation	22
	Summary	28
3.	First-Order Nonlinear Difference Equations: Processes of Social Diffusion	29
	Mobilization Through Social Interaction	29
	A Diffusion Model	30
	Parameter Restrictions	35
	Model Estimation	36
	An Empirical Example	37
	Analyzing the Model	38
	Equilibrium Analysis	39
	Local Stability Analysis	40
	Global Stability Analysis for Quadratic Recursive Forms	42
	Summary	44
4.	Linear Systems and Higher-Order Equations: Arms Races and Feedback Processes	45
	Higher-Order Models	45
	The Richardson Arms Race Model	46
	Arriving at a Second-Order Reduced Form	47
	Putting the Arms Race in Matrix Notation	48
	Finding the System Equilibrium	49
	Solutions for Higher-Order Systems	50
	Putting the Solution to Work	54
	Stability Conditions	55
	The Geometry of Stability: An Alternative Approach	56
	Feedback Time Delay as a Destabilizing Influence	60
	Summary	63
5.	Nonlinear Dynamic Systems: Budgetary Competition	65
	Incrementalism	65
	Competitive Models of Budgetary Interaction	66
	The Logic of Competition	68
Model 1	Unrestrained Budgetary Competition	70
Model 2	Restricted Competition	80
	Conclusion	81
6.	Dynamic Modeling as a Scientific Enterprise	81
	An Overview of Model Structure	82
	Multiple and Interdependent System States	83
	Structural Parameters	64
	System Properties	85
	Steps in Model Development	85
	Appendix	87
	Notes	91
	References	92