ANALYSIS OF PATTERN-FORMATION IN REACTION-DIFFUSION MODELS WITH SPATIALLY INHOMOGENOUS DIFFUSION-COEFFICIENTS

We consider a reaction diffusion system in one spatial dimension in wh ich the diffusion coefficients are spatially varying. We present a non -standard linear analysis for a certain class of spatially varying dif fusion coefficients and show that it accurately predicts the behaviour of the full nonlinear system near bifurcation. We show that the stead y state solutions exhibit qualitatively different behaviour to that ob served in the usual case with constant diffusion coefficients. Specifi cally, the modified system can generate patterns with spatially varyin g amplitude and wavelength. Application to chondrogenesis in the limb is discussed.