Strong resonances of a field of oscillators and defect bifurcation

Book excerpt: There are two subjects in this thesis. In the first part, a qualitative method to classify and predict the structure of defects in reaction-diffusion systems is introduced. This qualitative approach makes it easier to analyze the behavior of defects in complex systems. It also gives us information about the inner structure of the defect, and from that point of view, it makes it possible to approach the concept of defect bifurcation in a novel manner. In the second part, we study the normal form governing the evolution of a spatially extended homogeneous temporal instability, in the presence of a temporal forcing. This is equivalent to studying strong resonances of a field of nonlinear oscillators. A detailed analysis of the phase space of this normal form reveals a rich dynamical structure, which gives rise to a variety of spatial structures. These include excitable pulses, excitable spirals, fronts and spatially periodic structures. These structures are studied and their possible bifurcations are analyzed from a qualitative point of view.