Non Linear Evolution of Dynamic Spatial Systems: Lessons from Chaos and Niche Theory

Recently increasing interest in non-linear dynamic phenomena has emerged in economics and regional science, such as resilience of systems to sudden changes, adjustment processes, uncertainty and perturbations at both micro and macro levels. In the context of spatial modelling this has also provoked an increasing use of (continuous and discrete) dynamic models derived from ecology (such as May's logistic growth model which is able to generate chaotic behaviour, or prey-predator equations which are able to generate cycles or oscillating behaviour). Such models are able to depict both regular and irregular movements of spatially relevant phenomena. This paper aims to offer a comprehensive overview of recent developments in this field, with particular attention for spatial systems. Starting from a methodological review of central concepts of chaos theory and related modelling attempts, the present paper gives a survey of possible evolutions of dynamic spatial systems known from the literature (such as the class self-organizing systems from social sciences) by investigating the connections between ecology and (spatial) economics. In particular, ecological approaches based on niche theory and competition models will be dealt with from the viewpoint of the possibility of chaotic behaviour. Some simulation results will be added as well. The paper will conclude with further reflections on new research directions which need to be developed in regional science.