Dynamic Modeling: An Introduction (Quantitative Applications by R . Robert Huckfeldt;Carol W. Kohfeld;Thomas W. Likens

By R . Robert Huckfeldt;Carol W. Kohfeld;Thomas W. Likens

This brief monograph lays out the speculation in the back of, and methods for, utilizing dynamic modelling, taking the reader via a sequence of more and more complicated types. At each one step, examples are used to provide an explanation for the method, and likewise to explain particular functions of distinction equation versions within the social sciences. 'It is an efficient instance of classical mathematical version construction and that i could use it as a textual content for the direction on that topic in our MSc on Quantitative tools within the Behavioural Sciences...in normal it's to be recommended.' -- Bethlem and Maudsley Gazette, Vol 31 No 2, 1983

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Sample text

These distinctions sometimes cause difficulties when first encountered. To fix ideas, keep in mind that one and only one equilibrium value is determined for a specified set of parameter values. On the other hand, any given value for Mt may be considered an (arbitrary) initial condition. The model specifies the laws of behavior for mobilization in the short run, but the general theory of linear difference equations discloses that the short-run law has a long-run consequence, namely, the limiting or equilibrium value toward which the process has a tendency to move after any displacement.

By this we mean the laws of change that define the time-dependence of a process. The first objective of dynamic modeling is to understand, substantively, the mechanisms that are generating change in some observable phenomenon, and then to translate this set of ideas about structure into a mathematical language that can be deductively investigated. The techniques presented here are intended to equip the reader with a set of tools for representing dynamic structures and investigating how such structures behave.

The recursive form of this model, however, has been carefully analyzed, and it is possible to deduce its equilibria and qualitative behavior over time. ) Models of this form have been used to explore such diverse applications as political mobilization, the adoption of birth control practices, and the spread of policy innovations. Typical applications include: (1) population demography, (2) social contagion and the spread of contagious diseases, (3) rumor spread, and (4) rapid changes in public opinion.

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