Mathematics of organizationally complex systems.

Our approach to the development of an appropriate formalism for organizationally complex systems has been to search for a general formalism that would retain the essential nonlinear features (at least in approximate form) and yet would be amenable to mathematical analysis. The power-law formalism, described in detail elsewhere, leads naturally to a system of nonlinear differential equations, which is called an "S-system" because it captures the saturable and synergistic properties intrinsic to biological and other organizationally complex systems. Some of the advantages of this formalism and its implications for complex systems are discussed. Although the power-law formalism was originally developed as an "approximation", there are now several examples of "exact" representation by S-systems. In fact, a wide range of nonlinear equations can be recast in the form of S-systems. Such recasting and the use of algorithms optimized for S-systems greatly improves the efficiency of solution over that obtainable with conventional algorithms.