Extension of Levins loop analysis to transient and periodic disturbances

Levins´ Loop Analysis was developed for investigating the behavior of distributed, interconnected systems in which the interactions are not known well enough to completely model quantitatively, such as in many ecological communities. The presence or absence and the signs of the interactions between the subsystems may be all that is assumed in the model structure. The analysis focuses on the question of the qualitative stability, in the small, of the equilibrium points of the system as well as the possible first order shifts in these equilibrium points due to the influence of constantly acting disturbances. The Loop method is extended in this discussion to the qualitative analysis of the transient and long term tracking behavior of stable systems experiencing time-dependent and periodic disturbances.