title: Symmetries of S-systems.
abstract: An S-system is a set of first-order nonlinear differential equations that all have the same structure: The derivative of a variable is equal to the difference of two products of power-law functions. S-systems have been used as models for a variety of problems, primarily in biology. In addition, S-systems possess the interesting property that large classes of differential equations can be recast exactly as S-systems, a feature that has been proven useful in statistics and numerical analysis. Here, simple criteria are introduced that determine whether an S-system possesses certain types of symmetries and how the underlying transformation groups can be constructed. If a transformation group exists, families of solutions can be characterized, the number of S-system equations necessary for solution can be reduced, and some boundary value problems can be reduced to initial value problems.
authors.affiliation: Department of Biostatistics, Epidemiology, and Systems Science, Medical University of South Carolina, Charleston.
authors.forename: E O
authors.initials: EO
authors.lastname: Voit
mesh_terms: D008954:Models, Biological; D008962:Models, Theoretical; D013598:Systems Theory