Logarithmic Lipschitz norms and diffusion-induced instability
  This paper proves that contractive ordinary differential equation systems remain contractive when diffusion is added. Thus, diffusive instabilities, in the sense of the Turing phenomenon, cannot arise for such systems. An important biochemical system is shown to satisfy the required conditions. 
Zahra Aminzare and Eduardo D. Sontag
cs.SY math.AP