Contenido Descargable
Descargar PDFRichardson, George P.,"Loop Polarity, Loop Dominance, and the Concept of Dominant Polarity", 1984
- 1984
- Processing documentation available at: https://wiki.albany.edu/display/SCA/Processing+Ingested+Digital+Files
- Contact Us for questions or additional rights.
There is a conspicuous gap in the literature about feedback and circular causality between intuitive statements about shifts in loop dominance and precise statements about how to define and detect such important nonlinear phenomena. This paper provides a consistent, rigorous, and useful set of definitions of loop polarities, dominant polarity, shift in dominant polarity, and shift in loop dominance, and illustrates their application in a range of system dynamics models. Consistent with the usual intuitive definitions, the polarity of a first-order feedback loop involving a level x and a single inflow ẋ is defined to be the sign dẋ/dx. Loop polarity is shown to depend upon the sign of parameters not usually considered part of the loop itself. This expression of loop polarity is then applied to multi-loop first-order systems to define the polarity of such systems. All positive loops with gain less than one, such as economic multipliers, are shown to be multi-loop systems with dominant negative polarity. The shifts in loop dominance that occur in nonlinear systems arise naturally as changes in the sign of the dominant polarity. Examples applying the notion of dominant polarity reveal a useful geometric characterization of shifts in loop dominance in nonlinear first-order systems. The concepts developed in the paper are then applied to simple higher-order nonlinear feedback systems. The final application to a bifurcating system suggests that all bifurcations in continuous systems can be understood as consequences of shifts in loop dominance at equilibrium points.
This is the whole item.
ITEM CONTEXT
- This collection is part of the University Archives