### Abstract

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 language | English (US) |
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Pages (from-to) | 83-115 |

Number of pages | 33 |

Journal | Mathematical Biosciences |

Volume | 87 |

Issue number | 1 |

DOIs | |

State | Published - 1987 |

Externally published | Yes |

### ASJC Scopus subject areas

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

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## Cite this

*Mathematical Biosciences*,

*87*(1), 83-115. https://doi.org/10.1016/0025-5564(87)90035-6