How many variables? Some comments on the dimensionality of nonlinear systems
Voit, Eberhard O.
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While at first glance seemingly obvious, the number of variables in a model is not a priori fixed. For mathematical purposes, it is oftentimes convenient to reduce the number of variables to a minimum, but such reduction sometimes obscures meaning and insight and is not always computationally optimal. This is demonstrated with a special class of nonlinear differential equations, called S-systems, whose specific mathematical structure makes reduction as well as expansion of models translucent. The reduction shown here is based on the determination of Lie groups of scaling transformations, while the expansion is based on equivalent recasting. The Lie reduction constitutes the inverse operation to the recasting of multinomial systems.