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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]

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 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 PUBLISHER]

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]

In this paper we analyze the role of pollution for industry location and residence choice. We present a new economic geography (NEG) model in which manufacturing generates local pollution (that does not accumulate) and uses two types of labour input: unskilled workers that cannot migrate and work where they live; and high-skilled entrepreneurs that choose where to produce and where to live. Taking on board costless commuting or, in alternative, distance working, entrepreneurs can live in a different location from production. Both types of households enjoy utility from consuming all commodities (locally and imported variants) and suffer from local pollution. The resulting model is of the footloose entrepreneur variant, but involves two dynamic equations: the standard one governing the residential choice of entrepreneurs, and another one governing where production is located. The current paper analyses the discrete time dynamic process defined by a two-dimensional piecewise smooth map. Depending on parameters this map can have possibly coexisting attractors of various types (fixed points, cycles, closed curves as well as chaotic attractors). We analytically obtain stability conditions for the fixed points. Using numerical methods we describe also some global dynamic properties of the considered map. Finally, we propose an economic interpretation of the results concerning local stability analysis and global dynamics. [ABSTRACT FROM AUTHOR]

An abstract for the article "Online Chemical Modeling Environment (OCHEM): Web Platform for Data Storage, Model Development and Publishing of Chemical Information," by I. Sushko, A.K. Pandey, S. Novotarskyi, W. Teetz, S. Brandmaier, A. Abdelaziz, V.V. Prokopenko and colleagues is presented.

We develop a behavioral stock market model in which a market maker adjusts stock prices with respect to the orders of chartists, fundamentalists and sentiment traders. We analytically prove that the mere presence of sentiment traders, i.e. traders who optimistically buy stocks in rising markets and pessimistically sell stocks in falling markets, compromises the stability of stock markets. In particular, this means that instead of converging towards their fundamental value, stock prices either display endogenous oscillatory dynamics or converge towards nonfundamental fixed points – observations that challenge standard stability claims offered in the pertinent literature. [ABSTRACT FROM AUTHOR]