The attractiveness of the European South as described by a cusp and a butterfly catastrophe model

Over the past years a large number of regional growth theories have been developed and a number of models have been built in an effort to describe, explain and eventually predict regional development trends. However, until a few years ago, the large majority of those models assumed the existence of linear and thus regular, growth processes. Linear models are certainly able to generate unstable solutions, but the solutions of such models are restricted to certain regular standard types. This limitation has recently been overcome with the adoption of non-linear models which allow for a change in a system's dynamics generated by even small perturbations in structural forms. Structural instability entails the possible existence of significant qualitative changes in the behaviour of the system (i.e. in the state variables) closely connected with bifurcation and catastrophic phenomena that may occur if the parameter values (i.e. the control variable) reach critical values. The application of non-linear models has shown that the deterministic and well-behaved unique results achieved by the dynamic linear models are no longer guaranteed: interregional convergence determined by the traditional models collapses and opens the way to alternative possible trajectories and multiple equilibria. The non-linear models are thus able to simulate an endogenous series of complex phenomena which in the past could only be replicated by means of exogenous shocks introduced ad hoc. The present paper introduces a country's Image, a variable which expresses a country's state of development and its future prospects. Furthermore, the factors affecting this variable are defined and ways of measuring them are suggested. Finally, these factors are grouped into different ways leading to two alternative non-linear models for the generation of country's image. The two models are applied to the case of the European South and the values of the two sets of images for those countries are compared and discussed.