Nonlinearity

Chapter 6 discusses nonlinearity as the first fundamental complexity concept. Many phenomena of interest to complexity science and complexity economics are related to nonlinearity. At the same time, nonlinearity is so pervasive in the natural and social world that it should be considered the normal case. The first part of the chapter provides an introduction to the mathematics of nonlinear dynamics, which serves as background for the rest of the book. It is shown that continuous two-dimensional systems can have periodic orbits in addition to fixed points and bifurcations, at which the behavior of the system changes qualitatively. Furthermore, catastrophes and chaos are discussed. In the second part, two exemplary economic models that use this kind of mathematics are presented: a model of financial instability and a model of endogenous business cycles with nonlinear expectation formation. Finally, the role of nonlinearity in economics in general is discussed.