| Abstract: | The resistance of a nutrient cycling system to a disturbance that alters the flow rates, measured by the displacement of the nutrient levels while the disturbance continues, is as important an aspect of stability as the rate of return to equilibrium after the disturbance ends. Two important characteristics of the resistance of a system are the ultimate displacement that would occur if the disturbance lasted indefinitely, and the rate at which the system approaches the ultimate displacement.The mathematical theory is worked out for linear systems and applied to a group of eight nutrient cycling models. The relative resistance of individual compartments of different systems depends heavily on the period of interest, because of the wide range of magnitudes of the eigenvalues, which determine the response times. However, when measuring the change in total nutrients in a system with small exterior flows compared with the amount of internal cycling, only the critical root is significant in determining the response rate. |
