Absolute and convective instabilities
in 1D brusselator flow model
S.P. Kuznetsov and E. Mosekilde
Institute of Radio-Engineering and Electronics, Saratov, Russia
Technical University, Copenhagen, Denmark
We consider a spatially extended one-dimensional model of reaction-diffusion system with flow. It is assumed that the mixture of the reagents is pumped from the edge of the reaction space at x=0 and moves with constant velocity c. As a concrete example we study a Brusselator flow model governed by dimensionless equations
where U and V are the concentrations accounted as dynamical variables, 
is ratio of the diffusion coefficients for the corresponding species, A
and B are concentrations considered as control parameters.
While analyzing stability of homogeneous stationary solution U=A,
V=B/A, it is crucial to distinguish absolute and convective
character of two kinds of instabilities intrinsic to the system (Hopf
and Turing instabilities [1]). Using the approach of Bers and Briggs [2],
we find regions of absolute instabilities in the (B, c) parameter plane.
Different possibilities of mutual locations of domains are revealed in
dependence on rest parameters A and .
Numerical results of solution for the nonlinear equations are presented for the system with boundary conditions
Relation of the pattern formation process to character of the linear instability is discussed in details. The parameter domains are found where perturbations from the edge of the system do not damp in space given rise to stationary wave patterns. A possibility of experimental study of a variety of the revealed phenomena is emphasized.