SERIE RESEARCH mEmORMIDII

Dynamics of Generalised Spatia! Interaction Models This paper analyses dynamic properties of generalised spatial interaction models, w'rth particular emphasis on Alonso's generai theory of movements. Although the application of this theory addressed in the paper is a muitiregional demographic stock-flow model, it can easily be shown that the approach can be generalised to all types of spatial interaction phenomena. After an introduction to the Alonso model, it is demonstrated that various classes of spatia! interaction models (e.g., gravity and entropy models; doubly constrained trip distribution models) are specific cases of the generalised Alonso model. Next, the equilibrium and siability conditions of the spatial distribution resulting from the stock-flow model are further analysed. Although an analytical expression for the so-cailed systemic variables of the model is only possible under very restrlctive conditions, it is yet possible to study equilibrium and stability conditions more profoundiy by rewriting the generalised spatial interaction model as a general non-linear dynamic Volterra-Lotka model, so that stabie and unstable time trajectories can be examined. Furthermore, it appears to be possible to formulate more precise conditions that ensure Iocal stability in particular cases. In order to obtain more insight into the Iocal and global stability of the generalised spatial interaction model, simulation experiments are carried out with a muitiregional demographic stock-flow model for New Zealand. Various results are presented and discussed in the light of the above mentioned analysis.