A phase boundary separates different areas of phase space, for example the region of ordered dynamics from the region of chaotic dynamics. The region at or near this boundary is described as the complex area or regime.
According to the thesis of Stuart Kauffman's book, The Origins of Order parallel processing systems that lie in this interface region may be those best able to adapt and evolve. These poised systems appear to be best able to ccordinate complex, flexible behavior and best able to respond to changes in their environment. His study seeks to link natural selection and self-organization, and he proposes that natural selection may be the force that pulls adaptive systems to this boundary region.
see network Kauffman often characterizes the three regimes as solid or frozen (the ordered regime, as gas (the chaotic regime), and as liquid (the complex regime). More precisely, the complex regime (coming to it from the ordered regime) is thought of as a moment when the frozen regime is melting and tenuous and shifting relations are occuring between the unfrozen areas. In this sense it is not a true phase, like the liquid phase of matter, but a phase transition.
An example of phase transitions is the horse's walk, trot, gallop.
a phase singularity is a point at which phase is ambiguous and near which phase takes on all values. Time at the poles of the earth is an example. All the time zones converge. If you look at the sun to determine time, it circles at the same altitude along the horizon, and every direction is south (or north, depending on which pole) The poles are singularities for both time and space.
Deleuze and Guattari's distinction between the smooth and striated is an analogue of these dynamic regimes. It is interesting to note that the oceans (liquids) have been the perpetual site of contest between the smooth and the striated.