ABSTRACT
Chapters 14 and 15 present some very new methods for modeling complex systems. These new methods involve using nonlinear discrete time or differential equations. These nonlinear models generally can not be solved exactly, but require numerical and graphical methods for envisioning solutions. The new graphical methods will introduce some new language for describing complex systems, such as “phase space plots,” stable and unstable steady states,“null clines,” “bifurcation diagrams,” catastrophhes,“ hysterisis,” and so on. To date, these methods have been remarkably successful in a wide range of sciences in describing very complex systems with relatively few parameters, although their application in the social sciences has been limited so far. The advantage that these types of models have over the statistical models previously introduced in this book is that they permit simulations of the system under conditions different from those that generate the model. In this way, these models make it possible to consider systematic experiments or interventions that will test and further refine the model, and help understand how the system changes as a function of system parameters, varying initial conditions, and so on.
