In the phase representation they appear either as two-armed spirals or as targets. Defects confined to the domain walls are singularities of one of the two components of the vector field and they appear as truncated simple spirals. The topological character of the defects is clearly seen, for example, at the center of the two-armed phase spirals, where different phase values characterized by different colors meet. The oscillation phase is thus ill-defined and this is the reason why the oscillation amplitude vanishes there. Based on the values of the two independent phases in a closed path around the defects, two kinds of topological charges can be assigned to each of them, giving thereby a classification of these defects.
Topological constraints enforce charge conservation rules that greatly influence the dynamics.
A field configuration containing different kinds of vector topological defects for an oscillating medium in two spacial dimensions. Field configurations as the one shown in Figure 3a can freeze in a glassy state with slow dynamics or follow a spatiotemporally chaotic evolution. In any case, dynamics is essentially governed by the interactions of the topological defects that behave as particle-like objects. Defects, pulses, spiral waves, and intermittency are beautiful phenomena appearing in a variety of situations. Frequently they provide basic units from which more complex behavior is built up.