ON POTENTIALIZED PARTIAL FINITE DIFFERENCE EQUATIONS: ANALYZING THE COMPLEXITY OF KNOWLEDGE-BASED SPATIAL ECONOMIC DEVELOPMENTS

Knowledge-based regional and urban studies are plentiful; some systematics might be in order at this junction, so first the different links between economic production units in geographical space have to be clearly defined. Then a tool to represent the dynamics of those links should be selected; potentialized partial differential equations (PPDEs) are an appropriate tool to represent space-time relations in pre-geographical space. In practice, however, only discrete data are available, hence the question of how finite differences could generate PPFDEs (potentialized partial finite difference equations). A case has been worked out and simulated, showing a high degree of spatio-temporal complexity. Spatial econometric estimation is possible, as other work has shown; so an application to empirical data for France could be presented. Different versions of the latter have been worked out; they are presented in succession, followed by a last exercise on US data.