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We develop a foreign exchange market model in which a market maker adjusts the exchange rate with respect to the trading behavior of chartists, fundamentalists and a central bank. While chartists bet on the persistence of bull and bear markets, fundamentalists speculate on mean reversion. The central bank seeks to stabilize the foreign exchange market by placing buy (sell) orders when the undervaluation (overvaluation) of the exchange rate exceeds a certain threshold. Since a one-dimensional piecewise-linear discontinuous map with three branches determines the evolution of the exchange rate, we use a combination of analytical and numerical tools to explore the extent to which the central bank is able to tame the behavior of the foreign exchange market. [ABSTRACT FROM AUTHOR]

A 2D piecewise linear continuous two-parameter map known as the Lozi map is a special case of the 2D border collision normal form depending on four parameters. In the present paper, we investigate how the bifurcation structure of the Lozi map is incorporated into the bifurcation structure of the 2D border collision normal form using an analytical representation of the boundaries of the largest periodicity regions related to the cycles with rotation number 1/n, n ⩾ 3. At the centre bifurcation boundary of the stability domain of the fixed point both maps are conservative which leads to a quite intricate bifurcation structure near this boundary. [ABSTRACT FROM AUTHOR]

This paper contributes to studying the bifurcations of closed invariant curves in piecewise-smooth maps. Specifically, we discuss a border collision bifurcation of a repelling resonant closed invariant curve (a repelling saddle-node connection) colliding with the border by a point of the repelling cycle. As a result, this cycle becomes attracting and the curve is destroyed, while a new repelling closed invariant curve appears (not in a neighborhood of the previously existing invariant curve), being associated with quasiperiodic dynamics. This leads to a global restructuring of the phase portrait since both curves mentioned above belong to basin boundaries of coexisting attractors. [ABSTRACT FROM AUTHOR]

We present a linear New Economic Geography model with three regions, one remote region and two regions that entertain a trade agreement with low bilateral trade costs. Only one of these two integrated regions has the outside option to conclude an additional trade agreement with the remote region and to obtain a hub position. We show that the new trade agreement has a substantial impact on industry location and trade patterns and that the effects strongly depend upon level of integration between the initial two regions. It is not always the region with the outside option that profits from using it. Finally, we also show that higher firm mobility may lead to complex dynamics. [ABSTRACT FROM AUTHOR]

We consider a discrete-time version of the continuous-time fashion cycle model introduced in Matsuyama, 1992. Its dynamics are defined by a 2D discontinuous piecewise linear map depending on three parameters. In the parameter space of the map periodicity, regions associated with attracting cycles of different periods are organized in the period adding and period incrementing bifurcation structures. The boundaries of all the periodicity regions related to border collision bifurcations are obtained analytically in explicit form. We show the existence of several partially overlapping period incrementing structures, that is, a novelty for the considered class of maps. Moreover, we show that if the time-delay in the discrete time formulation of the model shrinks to zero, the number of period incrementing structures tends to infinity and the dynamics of the discrete time fashion cycle model converges to those of continuous-time fashion cycle model. [ABSTRACT FROM AUTHOR]

The main purpose of the present survey is to contribute to the theory of dynamical systems defined by one-dimensionalpiecewise monotone maps. We recall some definitions known from the theory ofsmoothmaps, which are applicable to piecewise smooth ones, and discuss the notions specific for the considered class of maps. To keep the presentation clear for the researchers working in other fields, especially in applications, many examples are provided. We focus mainly on the notions and concepts which are used for the investigation of various kinds of attractors of a map and related bifurcation structures observed in its parameter space. [ABSTRACT FROM PUBLISHER]

The goal of the present paper is to collect the results related to dynamics of a one-dimensional piecewise linear map widely known as the skew tent map. These results may be useful for the researchers working on theoretical and applied problems in the field of nonsmooth dynamical systems. In particular, we propose the complete description of the bifurcation structure of the parameter space of the skew tent map, providing the related proofs. It is also shown how these results can be used to classify border collision bifurcations in one-dimensional piecewise smooth maps. [ABSTRACT FROM AUTHOR]

The features of regularization method of ill-conditioned derivatives matrices from transfer resistances (nodal voltages) on surface zones conductivities solving the Electrical Impedance Tomography (EIT) reconstruction problems are considered. Using the proposed method allows significantly (hundreds of times) reduce the derivatives matrices orders in comparison to the classical phantom model using finite element method that noticeably simplifies the images reconstruction. The calculation examples show that for separate inhomogeneity visualization (geometric localization, size and character definition) it is sufficient to use the no iteration regularization by A. Tikhonov. The iteration regularization should be applied in cases when it is necessary to determine the absolute values of inhomogeneity conductivities with some precision; it requires a large number of iterations. The alternative method (for the last one) is the modification method for matrix inversion. The examples of inhomogeneity (in the center and in the edge of phantom) visualization are shown. [ABSTRACT FROM AUTHOR]