Complex Systems, Nonlinear Dynamics, and Local Activity Principle

Abstract

Jay Wright Forrester starts with models of complex social systems from the engineering and management side in 1950s, leading to applications in industrial, urban and even world dynamics. These models are clearly limited to equilibrium dynamics which is mathematically insufficient to understand the non-equilibrium dynamics of the world. Mathematically, we must consider the local activity of complex systems and their nonlinear dynamics. Therefore an alternative approach is suggested which gets along without microscopic equations, but nevertheless takes into account the local decisions and actions of individuals with probabilistic methods in order to derive the macrodynamics of social systems. The modeling design consists of three steps: In the first step appropriate variables of social systems must be introduced to describe the states and attitudes of individuals. The second step defines the change of behavior by probabilistic phase transitions of individual states. The third step derives equations for the global dynamics of the system by stochastic methods.