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

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.