3. Simplifying the model by rescaling

In the last Section the model has been explained. To make the following process easier to understand, the equations are shown again in the next figure.

[differential equations] (1a-c)

This System can be transformed in a simpler one. The system of the dynastic cycle can be rescaled in order to reduce the number of parameters. This is done by defining a new time variable tau as follows:

[tau = rt]

and by defining new parameters by:

[x=X/k; y=aY/(rk); z=acZ/(kmr); B=b/k; H=hmk/(ac);
Q=m/r; E=ae/m; D=ad/(rk); R=acf/(mr); G=gm/(acf);]

These two steps reduce the system to the following form:

[simpler differential equations] (2a-c)

A deep understanding of this system can be obtained if the subsystem (x,y) is first analyzed by considering z as a parameter. This will be done in the next Section.

Last updated on June 24, 1997 by Helmut Doleisch (helmut@cg.tuwien.ac.at)