The geometrical metaphor of centre and periphery is often used to describe opposition between the two basic types of places in a system : the one which is commanding and benefitting it, the centre, and those which are subjected to it, in a peripheral position. This conceptual pair goes back at least to the time of Werner Sombart (Der moderne Kapitalismus, 1902), if not of Marx (city/countryside relations), and was used by the imperialism theoreticians (Rosa Luxemburg, Boukharine) but its contemporaneous form was given by economists specialised in development inequalities (Samir Amin, Le développement inégal, 1973). Alain Reynaud developed the notion in the field of geography (Société, espace et justice, 1981).
It is thus rigorous to avoid using these terms in their common sense, which is used in particular about urban realities, in order to distinguish what is in the middle from what is outside. There should be particular caution about representations in form of rings fitted inside each other, which may point as well to simple discretisations (rings of increasing or decreasing densities), to successive stages (rings of urban growth, for example), to distribution of phenomena of various nature in function of a distance parameter (rings of Thünen), as to an opposition between dominating and dominated places.
The concept may be used at all levels of the geographic scale (centre and periphery of a village farmland, of a city, of a region, etc.). But it has registered a particular success at the global level, as an equivalent of the “developed world / underdeveloped world” or “North / South” pairs. Centre / Periphery allows description of the opposition of places but moreover proposes an explanatory model of this differentiation : periphery is subjected because centre is dominating - and reciprocally. This concept has thus been mostly used in the context of third-worldist thinking, more or less as an instrument for making inhabitants of Western countries feel guilty. This is an excessively restrictive use of a much more efficient notion. To think in terms of centre(s) and periphery(ies) allows to reflect on interactions between places in the World : links of reciprocal dependency where inequalities are the rule, but which are not working one-way.
For the pair to make sense, there must be relationships between the two types of places, thus flows (of persons, goods, money, information, decisions,...) and these relationships must be dissymmetrical, (unbalance of flows, hierarchy of power relationships,...). The centre is central precisely because it benefits from this inequality and, in turn, the periphery(ies) is(are) characterised by a deficit which maintains its(their) dominated position. The hereby described system is auto-regulated : the centre reproduces conditions for its centrality and the periphery does the reverse. It is thus a pleonasm to talk about a “dominated periphery”. However, precisely because it is based on a logic of (inequal) exchange, the system is dynamic. Whereas some peripheries may become “dead ends” (they are then said « abandoned »), others may benefit from their situation (advantage on the long-run because of a greater size, of a location in contact with the outside of the spatial system,...); this can generate either polarity reversals in a logic that remains globally identical or system changes.
The centre/periphery model has thus a robust heuristic potential, provided it is not overused. Its use should be reserved to formalisation of any system based on inequality relationships, and it should not be used as a simple descriptor of spatial gradient or differentiation.