The maximum amplification of perturbations in ecological systems

Abstract

Conventionally, most researches of ecological models focus mainly on the asymptotic stability properties near equilibria. However, transient effects can be important. It dominates the dynamics seen in experimental or field studies. Transient behavior near an equilibrium is measured by resilience, reactivity, the maximum amplification of a perturbation and the time at which the maximum amplification occurs. In this paper, we demonstrate emphatically the calculation of the amplification envelope of a homogeneous system of linear equations, then apply it to three ecological models. We conclude that transient amplification of perturbations to a stable equilibrium should be a very common ecological phenomenon, and reactive systems have huge changes around their equilibria.