A propos Brexit: on the breaking up of integration areas – an NEG analysis

Inspired by Brexit, the paper explores the effects of splitting an integration area or "Union" on trade Patterns and the spatial distribution of industry. A linear three-region New Economic Geography (NEG) model is developed and two possible situations before separation are considered: agglomeration and dispersion. By analogy with the Brexit options, soft and hard separation scenarios are considered. Firms in the leaving region may move to the larger Union market, even on the periphery, relocation substituting trade; or firms in the Union may move in the more isolated leaving region, escaping from competition. The paper also analyses deeper Union integration following separation. Instances of multistability and complex Dynamics are found

Boolean Dynamics with Random Couplings

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the sizes of their basins of attraction, and the flow of information through the systems. In the limit of infinite N, there is a phase transition between a chaotic and an ordered phase, with a critical phase in between. We argue that the behavior of this system depends significantly on the topology of the network connections. If the elements are placed upon a lattice with dimension d, the system shows correlations related to the standard percolation or directed percolation phase transition on such a lattice. On the other hand, a very different behavior is seen in the Kauffman net in which all spins are equally likely to be coupled to a given spin. In this situation, coupling loops are mostly suppressed, and the behavior of the system is much more like that of a mean field theory. We also describe possible applications of the models to, for example, genetic networks, cell differentiation, evolution, democracy in social systems and neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical Sciences Serie