PySD: System Dynamics Modeling in Python

Abstract

System Dynamics (SD) is a mathematical approach used to describe and simulate the dynamics of complex systems over time. The foundations of the methodology were laid in the 1950s by Professor Jay W. Forrester of the Massachusetts Institute of Technology (Forrester, 1971). The building blocks of SD models are stocks, flows, variables, parameters, and lookup tables. Stocks represent cumulative quantities which take a certain value at each moment in time (integral), and flows are the rates at which those quantities change per unit of time (derivative). Variables express intermediate calculations, parameters set external conditions for the simulation, and lookup tables are single-valued functions that accept another model component as an argument. These components can combine to create feedback loops in which the state of the stock variables feeds back to influence flows in the model. The relationships between these model components can be represented using causal loop diagrams, see Figure 1.