Differential-flow-induced instability in a cubic autocatalator system

摘要: The formation of spatio-temporal stable patterns is considered for a reaction-diffusion-convection system based upon the cubic autocatalator, A + 2B → 3B, B C, with reactant being replenished by slow decay some precursor P via simple step A. reaction in differential-flow reactor form ring. It assumed that immobilised within and autocatalyst allowed to flow through constant velocity as well able diffuse. linear stability spatially uniform steady state (a, b) = (µ−1, µ), where b are dimensionless concentrations B, µ parameter reflecting initial concentration P, discussed first. shown necessary condition bifurcation this stable, non-uniform, flow-generated φ > φc(µ, λ) φc(µ,λ) (strictly positive) critical value λ diffusion coefficient species also reflects size system. Values φc at which these bifurcations occur derived terms λ. Further information about nature bifurcating branches (close their points) obtained from weakly nonlinear analysis. This reveals both supercritical subcritical Hopf possible. then followed numerically means path-following method, parameter, representatives values found multiple can exist it possible any lose secondary bifurcations. typically gives rise quasiperiodic transients ultimately attracted one remaining available patterns.