Generalized models as a universal approach to the analysis of nonlinear dynamical systems

We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can describe a class of systems which share a similar structure. Despite this generality, the proposed approach allows us to study the dynamical properties of generalized models efficiently in the framework of local bifurcation theory. The approach is based on a normalization procedure that is used to identify natural parameters of the system. The Jacobian in a steady state is then derived as a function of these parameters. The analytical computation of local bifurcations using computer algebra reveals conditions for the local asymptotic stability of steady states and provides certain insights on the global dynamics of the system. The proposed approach yields a close connection between modelling and nonlinear dynamics. We illustrate the investigation of generalized models by considering examples from three different disciplines of science: a socio-economic model of dynastic cycles in china, a model for a coupled laser system and a general ecological food web.Comment: 15 pages, 2 figures, (Fig. 2 in color

Enlargement of the European Union: A movement towards the optimal trade bloc size?

This paper analyses how the enlargement of a trade bloc will affect national welfare. We establish a partial equilibrium model of a trade bloc either operating as a monopoly with a competitive fringe or facing a duopolistic game in production taxes/subsidies. Given this framework, we demonstrate how member countries’ welfare effects depend on their trade flow and the market power of the trade bloc. A numerical estimation of the effects of EU enlargement on the major grain crop markets suggests that welfare effects are negligible. Economic reasons are therefore unlikely to be a motivating force for further enlargement.trade bloc, trade liberalisation, game theory, European Union, International Relations/Trade, D42, F11, Q17, Q18,