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 meaningful 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 behavior. In addition, the present paper also analyses the impact of this dynamic logit model upon a more general spatial system, notably a Lotka-Volterra system in the context of a transportation network including congestion phenomena. Time lags are also incorporated in order to account for non-instantaneous effects in prey-predator type of interactions. Finally, it is shown that under certain conditions on the parameters of the spatial system concerned a so-called Hopf bifurcation takes place. In other words, unstable systems behaviour may emerge for particular lag values reflecting the influence from the past. The theoretical analysis in the paper is illustrated by means of various simulation experiments.