Pattern formation through reaction and diffusion in a simple pooled-chemical system

摘要: The formation of spatial patterns is considered for a reaction-diffusion system based upon the cubic autocatalator, A+2B→3B, B→C, with reaction taking place inside closed vessel, reactant A being replenished by slow decay precursor P via simple step P→A. Patterns are shown to form only when dimensionless diffusion coefficient λ sufficiently small, number available increasing as diminishes zero. Two types occur, standing-wave arising out Hopf bifurcations, together steady-wave pitchfork bifurcations. local behaviour on bifurcating branches obtained weakly nonlinear theory. Close its point bifurcation, each pattern be partially stable; that is, it remains stable small disturbances composed own, or any higher spacial wave numbers. However, unstable smaller than own. This partial stability in line ...