System dynamics and world
System dynamics has its roots in systems of difference and differential equations (Forrester 1980: Section 3.3). A target system, with its properties and dynamics, is described using a system of equations which derive the future state of the target system from its actual state. System dynamics is restricted to the macro level in that it models a part of reality (the ‘target system’) as an undifferentiated whole, whose properties are then described with a multitude of attributes in the form of ‘level’ and ‘rate’ variables representing the state of the whole target system and its changes, respectively.
The typical difference equation has the form
where xt+1 is the state of the target system at time t + 1, which depends on its state at time t and on a parameter ϑ. Both x and ϑ may be vectors, that is, consist of several elements. f is usually a continuous function. Only in rare cases can the difference equation be solved explicitly to yield an expression for xt as a function of t and x0.
The typical differential equation has the form
where ẋ(t) is the state change of the target system within an infinitesimally short period of time dt. The amount of change depends on the state x(t) at
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Publication information: Book title: Simulation for the Social Scientist. Edition: 2nd. Contributors: Nigel Gilbert - Author, Klaus G. Troitzsch - Author. Publisher: Open University Press. Place of publication: Maidenhead, England. Publication year: 2005. Page number: 28.
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