Reactivity of communities at equilibrium and periodic orbits

Abstract

Reactivity measures the transient response of a system following a perturbation from a stable state. For steady states, the theory of reactivity is well developed and frequently applied. However, we find that reactivity depends critically on the scaling used in the equations. We therefore caution that calculations of reactivity from nondimensionalized models may be misleading. The attempt to extend reactivity theory to stable periodic orbits is very recent. We study reactivity of periodically forced and intrinsically generated periodic orbits. For periodically forced systems, we contribute a number of observations and examples that had previously received less attention. In particular, we systematically explore how reactivity depends on the timing of the perturbation. We then suggest ways to extend the theory to intrinsically generated periodic orbits. We investigate several possible global measures of reactivity of a periodic orbit and show that there likely is no single quantity to consistently measure the transient response of a system near a periodic orbit.