Explaining after by before: Basic aspects of a dynamic systems approach to the study of development
Section snippets
Dynamic systems gets you into problems…
Being a developmental psychologist and applying dynamic systems theory is almost like begging for trouble. A quick look through handbooks on dynamic systems theory (for instance Jackson, 1991, Katok and Hasselblatt, 2005) reveals an amassment of abstract terms and mathematical equations most of which are simply not accessible for the mathematically untrained reader, which the developmental psychologist is likely to be. It gets worse if instead of the handbooks the real mathematicians working in
The study of development: Two basic equations
The two basic equations that will be discussed in this section reflect an almost paradigmatical difference in the approach to development. In this light, it is worthwhile to give some thought to the original meaning of the word “development.” Etymologically, the English word development stems from the Old French desvoloper, which means “to unwrap.” The German and Dutch words Entwicklung and ontwikkeling are literal translations of that term. The word is also related to the Latin evolutio (to
The basic equation of dynamic systems
The CRC Concise Encyclopedia of Mathematics (Weisstein, 1999) provides a particularly helpful—and remarkably frugal—definition of a dynamic system. It defines it as “… a means of describing how one state develops into another state over the course of time” (Weisstein, 1999, p. 501) . Thus, if yt is a specification of a “state” of a variable y at time t, a dynamic model takes the formwhich should be read as “the value of y at time t + 1 is a function “f” of the value of y at time t.”
Results from the agent model
The second, i.e., agent model consists of a considerably more extensive set of coupled dynamic equations than the first model. The equations are referring to model components such as preference, emotional evaluation, coupling with emotional expression, effect of the other child’s action, effect of emotional expression and so forth. The relations between the components are represented graphically in Fig. 4. The arrows refer to simple quantitative relationships. White arrows refer to
Conclusion and discussion
A major goal of this article was to show that what we have—somewhat unscientifically—called the Groningen brand of dynamic systems might contribute to the understanding of developmental processes. The main idea of our approach was cast in the form of an elementary dynamic equation, which was compared with the elementary equation that underlies the majority of developmental research (which we called the standard approach). The latter equation represents an association between an independent
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