Recasting nonlinear differential equations as S-systems: a canonical nonlinear form

Michael A. Savageau, Eberhard O. Voit

Research output: Contribution to journalArticlepeer-review

221 Scopus citations


An enormous variety of nonlinear differential equations and functions have been recast exactly in the canonical form called an S-system. This is a system of nonlinear ordinary differential equations, each with the same structure: the change in a variable is equal to a difference of products of power-law functions. We review the development of S-systems, prove that the minimum for the range of equations that can be recast as S-systems consists of all equations composed of elementary functions and nested elementary functions of elementary functions, give a detailed example of the recasting process, and discuss the theoretical and practical implications. Among the latter is the ability to solve numerically nonlinear ordinary differential equations in their S-system form significantly faster than in their original form through utilization of a specially designed algorithm.

Original languageEnglish (US)
Pages (from-to)83-115
Number of pages33
JournalMathematical Biosciences
Issue number1
StatePublished - 1987
Externally publishedYes

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics


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