SERIE RE5EHRCH RIEmORRnDH CHAOS THEORY AND SPATIAL DYNAMICS

The theory of chaos is nowadays receiving a great deal of attention among social scientists. Many attempts are being made to offer a raeaningful interpretation and application of notions of chaos in social systems. The present paper aims to link chaos theory to spatial interaction analysis by focusing attention on the conditions under which a general utility function related to a dynamic logit model for spatial interaction analysis will exhibit chaotic behaviour. In addition, the present paper will also analyze the impact of this dynamic logit model upon a more general spatial system, notably a LotkaVolterra system in the context of a transportation network including congestion phenomena. Time lags will also be incorporated in order to account for non-instantaneous effects in prey-predator type of interactions. Finally, it will be shown that under certain conditions on the parameters of the spatial system concerned a so-called Hopf bifurcation will take place. In other words, unstable system's behaviour may emerge for particular lag values reflecting the influence from the past. The theoretical analysis in the paper will be illustrated by means of various simulation experiments.