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