Acoplamiento y Caos: un Análisis Matemático del Modelo de Dos Brusselators Acoplados

The Brusselator is a theoretical model that represents a type of autocatalytic chemical reaction with oscillations. The interaction between two Brusselators (coupled by diffusion) is described by the two-coupled Brusselators model. This model has at least one equilibrium point (in some regions of the parametric space there are up to four more equilibrium points) and undergoes a pitchfork and two saddle-node bifurcations under certain conditions.There are 4-dimensional nilpotent singularities of codimension 4 that are unfolded by the system of the two-coupled Brusselators. In any generic unfolding of such singularities there exist 3-dimensional nilpotent singularities of codimension 3 which are generically unfolded by the same family. As Shil'nikov homoclinic orbits exist in any unfolding of a 3-dimensional nilpotent singularity of codimension 3, these homoclinic orbits are present in the two-coupled Brusselators model. The existence of this type of homoclinic orbits implies the presence of strange attractors in a model. Therefore, the two-coupled Brusselators model contains strange attractors. The two-coupled Brusselators model is chaotic in some regions of the parametric space.