Pattern formation in Delayed Dynamical Systems

摘要

Understanding the spontaneous formation of spatial structures in nonlinear systems represents one of the chal-lenging problems in equilibrium thermodynamics. Although the most relevant phenomena occur in three dimensions and despite the dimensionality plays a central role in singling out the mechanisms of pattern selection, it is useful to investigate low-dimensional dynamics. In fact, this allows simulating larger systems and, in turn, coming closer to the thermodynamical limit, an ideal situation in which general theoretical results are more likely to be obtained. One of the disadvantages of studying low-dimensional and in particular one-dimensional systems is the difficulty of obtaining convincing experimental results. In fact, what one typically does is to impose a geometry such that one linear dimension is much larger than the others (e.g. an anular geometry in the study of hydrodynamic convection).