Abstract
A reaction-diffusion system, based on thecubic autocatalytic reaction scheme, with the prescribedconcentration boundary conditions is considered. The linearstability of the unique spatially homogeneous steady state solutionis discussed in detail to reveal a necessary condition for thebifurcation of this solution. The spatially non-uniform stationarystructures, especially bifurcating from the double eigenvalue, arestudied by the use of Lyapunov-Schmidt technique and singularitytheory. Further information about the multiplicity and stability of the bifurcationsolutions are obtained. Numerical examples are presented to supportour theoretical results.
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