Abstract
In this paper the behaviour of small solutions in a reaction-diffusionmodel problem is studied near a co-dimension 2 point. The normal form theory for reversible vector fields is applied on the stationary part of the reaction-diffusion system. This normal form is reduced to a 3-dimensional ODE that iscompletely integrable. An explicit expression for the solutions to the ODE andtherefore for the reaction-diffusion system is given under certain conditions.These solutions have the same multi-bump pattern as the asymptotically stablestationary multi-bump solutions that were found in the numerical simulationsof the full reaction-diffusion system.
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