Memory and Spatial Coupling in Regional Population Dynamics. A Fractional-Order Geosimulation of Regions

Regional population trajectories depend on the memory of past regimes and on interaction between neighbours. This study proposes a geosimulation in which the annual population of each NUTS-3 region follows a fractional-order Verhulst–Lotka–Volterra system on the regional graph. Each region has its own growth rate, carrying capacity and Caputo derivative order between 0.3 and 1.95, so that memory becomes a mappable parameter, and a gravity-type coupling lets neighbouring populations affect growth. The model is calibrated on Eurostat series for the 42 regions of Romania (2000–2025) as a coupled system, without coupling for 1,070 regions of the European Union and EFTA (2003–2023), and as coupled systems for Bulgaria and Lithuania, which with Latvia complete Europe’s four steepest-declining countries. Nested integer-order and uncoupled variants are compared with information criteria, identifiability analysis and rolling-origin forecasts. Freeing the order reduces the Romanian residual error 7.9-fold, and the fractional model is preferred for 79% of European regions. Orders are mostly inertial and strongly clustered in Europe (Moran’s I = 0.38) but not in Romania (I = −0.16). Coupling improves the fit in 36 of 42 Romanian regions, but a placebo test shows that the distance-decay form of the weights is not identified. Bulgaria, Lithuania and Latvia need memory as much as Romania, whereas coupling is spatially identified only in Romania, weak in Bulgaria and absent in Lithuania. Memory-based forecasts match extrapolation but not a five-year drift. The 2035 baseline projects a 3.9% national decline, growth around the capital and decline in the south.