On global stability of the Lotka reactions with generalized mass-action   kinetics
  Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions with two chemical species and arbitrary power-law kinetics. We study existence, uniqueness, and stability of the positive equilibrium, in particular, we characterize its global asymptotic stability in terms of the kinetic orders. 
Bal\'azs Boros, Josef Hofbauer, Stefan M\"uller
math.DS q-bio.MN