Memoranda Space - Time Dynamics , Spatial Competition and the Theory of Chaos

In economics and regional science we observe recently a growing interest in the use of non-linear dynamic models. In particular nonlinear deterministic models appear quite appealing, since they may exhibit both oscillating and chaotic behaviour and hence may provide an endogenous explanation of the periodicity and/or irregularity observed in the dynamics of spatial economie systems. In this paper the aim is to analyse consequences of spatial dynamic competition in regional systems including the possibility of chaotic behaviour. Non-linear deterministic models often used in ecology and biology will be investigated in this framework. Although these models by definition do not display oscillating behaviour, it will be shown that the particular case of a 'chaotic' evolution of May-type in one region will lead to an oscillating divergent behaviour in the entire system, if the intrinsic growth rates of the competing regions exceed a critical value (beyond which instability begins). The analysis will be illustrated by means of simulation experiments for both the cases of two and three competing regions.