### Abstract

A novel approach to the development of an appropriate formalism for representing organizationally complex systems began in the mid 1960's with a search for a general systematic formalism that would retain the essential nonlinear features and that would still be amenable to mathematical analysis. The set of nonlinear differential equations that most closely approached this goal was called an "S-system", because it accurately captures the saturable and synergistic properties intrinsic to biological and other organizationally complex systems. In the early 1980's it was found that essentially any nonlinear differential equation composed of elementary functions could be recast exactly as an S-system. Thus, S-systems may be considered a canonical form with the ability to represent an enormous variety of nonlinear differential equations. This has given rise to new strategies for the mathematical modeling of nonlinear systems.

Original language | English (US) |
---|---|

Pages (from-to) | 546-551 |

Number of pages | 6 |

Journal | Mathematical and Computer Modelling |

Volume | 11 |

Issue number | C |

DOIs | |

State | Published - 1988 |

Externally published | Yes |

### Fingerprint

### Keywords

- Canonical nonlinear forms
- differential equations
- organizationally complex systems
- strategies for nonlinear modeling
- synergistic systems

### ASJC Scopus subject areas

- Computer Science (miscellaneous)
- Information Systems and Management
- Control and Systems Engineering
- Applied Mathematics
- Computational Mathematics
- Modeling and Simulation

### Cite this

*Mathematical and Computer Modelling*,

*11*(C), 546-551. https://doi.org/10.1016/0895-7177(88)90553-5

**Introduction to S-systems and the underlying power-law formalism.** / Savageau, Michael A.

Research output: Contribution to journal › Article

*Mathematical and Computer Modelling*, vol. 11, no. C, pp. 546-551. https://doi.org/10.1016/0895-7177(88)90553-5

}

TY - JOUR

T1 - Introduction to S-systems and the underlying power-law formalism

AU - Savageau, Michael A.

PY - 1988

Y1 - 1988

N2 - A novel approach to the development of an appropriate formalism for representing organizationally complex systems began in the mid 1960's with a search for a general systematic formalism that would retain the essential nonlinear features and that would still be amenable to mathematical analysis. The set of nonlinear differential equations that most closely approached this goal was called an "S-system", because it accurately captures the saturable and synergistic properties intrinsic to biological and other organizationally complex systems. In the early 1980's it was found that essentially any nonlinear differential equation composed of elementary functions could be recast exactly as an S-system. Thus, S-systems may be considered a canonical form with the ability to represent an enormous variety of nonlinear differential equations. This has given rise to new strategies for the mathematical modeling of nonlinear systems.

AB - A novel approach to the development of an appropriate formalism for representing organizationally complex systems began in the mid 1960's with a search for a general systematic formalism that would retain the essential nonlinear features and that would still be amenable to mathematical analysis. The set of nonlinear differential equations that most closely approached this goal was called an "S-system", because it accurately captures the saturable and synergistic properties intrinsic to biological and other organizationally complex systems. In the early 1980's it was found that essentially any nonlinear differential equation composed of elementary functions could be recast exactly as an S-system. Thus, S-systems may be considered a canonical form with the ability to represent an enormous variety of nonlinear differential equations. This has given rise to new strategies for the mathematical modeling of nonlinear systems.

KW - Canonical nonlinear forms

KW - differential equations

KW - organizationally complex systems

KW - strategies for nonlinear modeling

KW - synergistic systems

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UR - http://www.scopus.com/inward/citedby.url?scp=38249032720&partnerID=8YFLogxK

U2 - 10.1016/0895-7177(88)90553-5

DO - 10.1016/0895-7177(88)90553-5

M3 - Article

AN - SCOPUS:38249032720

VL - 11

SP - 546

EP - 551

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

SN - 0895-7177

IS - C

ER -