Growth equations: A general equation and a survey of special cases

Abstract

Although growth in its various manifestations has been studied for centuries and although there are a large number of well-established growth "laws," that work is almost entirely empirical and lacks a theoretical foundation with which macroscopic aspects of growth might be related to underlying, microscopic determinants. Recent work on the analysis of complex systems, however, has provided just such a foundation. It has been shown that an important class of complex systems can be accurately described by a formalism involving simple nonlinear approximations. This formalism leads naturally to a general growth equation in differential form for complex systems. The survey of well-established growth equations presented here demonstrates that each of these is a special case of the general growth equation.