  The concept of limiting step gives the limit simplification: the whole
network behaves as a single step. However, in its simplest form this idea is
applicable only to the simplest linear cycles in steady states. For such the
simplest cycles the nonstationary behaviour is also limited by a single step,
but not the same step that limits the stationary rate. We develop a general
theory of static and dynamic limitation for all linear multiscale networks. New
estimates of eigenvectors for diagonally dominant matrices are used.
  Multiscale ensembles of reaction networks with well separated constants are
introduced and typical properties of such systems are studied. For any given
ordering of reaction rate constants the explicit approximation of steady state,
relaxation spectrum and related eigenvectors ("modes") is presented. The
obtained multiscale approximations that we call "dominant systems" are
computationally cheap and robust. These dominant systems can be used for direct
computation of steady states and relaxation dynamics, especially when kinetic
information is incomplete, for design of experiments and mining of experimental
data, and could serve as a robust first approximation in perturbation theory or
for preconditioning.
