1,721,038 research outputs found
Critical curves and bifurcations of absorbing areas in a financial model
No full textIn this paper the method of critical curves, a tool for the analysis of the global dynamical properties of two-dimensional noninvertible maps, is applied to study the dynamics of speculative markets, based on the interaction of different types of traders. The main purpose of the paper is to stress the role played by absorbing areas, particular trapping regions bounded by portions of critical curves, in the qualitative changes of the attracting sets and of the basins of attraction. Such kind of analysis is performed through an interplay among analytical, geometrical and numerical techniques
Multi-sector dynamics with nonlinear investment demand and scale-dependent input requirements
No full textlago di Gard
Cross-section instability in financial markets: impatience, extrapolation, and switching
Full text linkThis paper presents a stylized model of interaction among boundedly rational heterogeneous agents in a multi-asset financial market to examine how agents’ impatience, extrapolation, and switching behaviors can affect cross-section market stability. Besides extrapolation and performance based switching between fundamental and extrapolative trading documented in single asset market, we show that a high degree of ‘impatience’ of agents who are ready to switch to more profitable trading strategy in the short run provides a further cross-section destabilizing mechanism. Though the ‘fundamental’ steady-state values, which reflect the standard present-value of the dividends, represent an unbiased equilibrium market outcome in the long run (to a certain extent), the price deviation from the fundamental price in one asset can spill-over to other assets, resulting in cross-section instability. Based on a (Neimark–Sacker) bifurcation analysis, we provide explicit conditions on how agents’ impatience, extrapolation, and switching can destabilize the market and result in a variety of short and long-run patterns for the cross-section asset price dynamics
Coexistence of attractors and homoclinic loops in a kaldor-like business cycle model
No full textCoexistence of attractors is often a characteristic feature of economic models represented by nonlinear dynamic systems [see, among others, Agliari et al (2002), Bischi & Kopel (2001), Dieci et al (2001), Agliari et al (2000)]. Generally speaking, when multiple attractors coexist in the phase-space for a particular choice of the parameters of the model, a crucial question is about the role played by the initial conditions in determining the asymptotic behavior of the system. Moreover, in order to perform a proper bifurcation analysis with respect to some specific parameters it is necessary to take into account that parameter variations determine in general both qualitative changes (including appearance/disappearance) of the attractors, and structural changes of the basins of attraction of the coexisting attractors. The latter point has been less emphasized in the economic literature. In general, typical features of such qualitative changes of the basins are the following: (a) they are due to global bifurcations (not associated with the eigenvalues of the linearized system around a particular steady state) and (b) they may bring about a kind of "complexity" which is different from the one usually reported in the literature (associated with "strange attractors", and "sensitivity to initial conditions"): Namely, simple attractors (steady states, cycles of low period, attracting closed curves) may have basins with complex structures. In recent years, several studies have pointed out particular mechanisms of basin bifurcations, which are associated with contacts between basin boundaries and "critical sets", in the case of dynamical systems represented by the iteration of noninvertible maps [Mira et al (1996), Agliari et al (2002), Agliari (2001)]. Other possible mechanisms, which may occur in the case of invertible maps as well, are associated with homoclinic tangencies of the stable and unstable manifolds of saddles. The present Chapter illustrates the latter type of phenomena, in situations of coexisting attractors that arise from a particular version of Kaldor's business cycle model in discrete time, described by a nonlinear two-dimensional dynamical system. The particular Kaldor-like model at hand, where consumption is modelled as an S-shaped function of income, and investment is a linear increasing function of output (and a linear decreasing function of capital), has been developed in Herrmann (1985), and studied also in Lorenz (1992, 1993), Dohtani et al (1996), mainly in order to prove the emergence of chaotic dynamics in Kaldor-like models under extreme values of the output adjustment parameter. However, the particular parameter constellation which is assumed within the present Chapter (under which multiple equilibria exist) has been excluded from the analysis carried out in earlier work, though it corresponds to economically meaningful situations. We will show that for this choice of parameters, business fluctuations along a stable closed curve (which typically arise in Kaldor model), coexist with alternative dynamic outcomes (stable steady states, or stable periodic orbits of low period), which the system may reach in the long-run depending on the initial state. Furthermore, we will explain the bifurcation mechanisms which determine such situations of coexistence, the appearance or disappearance of attractors and the qualitative changes of the basins of attraction. The global dynamic phenomena which are detected in this Chapter are described in Chapter 1 and have also been detected in a different version of the Kaldor model in discrete-time [see Bischi et al (2001) and Agliari et al (2005b)], where investment is an increasing S-shaped function of output (and depends negatively on capital stock) and savings depend linearly on income. Therefore such dynamic phenomena seem to be very persistent ones, and their occurrence seems to be ultimately related to the following basic assumptions: (i) investment or consumption have sigmoid shaped graphs, in a way that the marginal propensity to invest is larger (smaller) than the marginal propensity to save for normal (extreme) levels of income, and (ii) the investment schedule shifts downwards (upwards) as output increases (decreases) as a result of a negative dependence on accumulated stock of capital. Both these assumptions are essential qualitative features of Kaldor's original model. On the other hand, very similar dynamic phenomena have been detected also in Agliari et al (2005a), where a two-dimensional map with a "minimal" structure qualitatively similar to that in Agliari et al (2005b), and to the one being studied here, has been analyzed in details. Further examples are shown in this book. Chapters 9 and 11. The Chapter is organized as follows. In Section 8.2 we present the business cycle model, perform useful changes of coordinates, and reduce it to a twodimensional map. Section 8.3 presents some general properties of the map, namely the symmetry, the steady states and local asymptotic stability conditions, and the conditions for invertibility. Section 8.4 focuses on particular global bifurcations, involving qualitative changes of the basins of attraction, occurring in a particular regime of parameters where three equilibria exist, and relates these phenomena to the behavior of the stable and unstable manifolds of saddles. © Springer-Verlag BerHn Heidelberg 2006
Production delays, technology choice and cyclical cobweb dynamics
Full text linkWe develop a cobweb model in which firms, facing a two-period production delay, have access to a flexible (costly) and an inflexible (cheap) production technology. Moreover, firms select between production technologies depending on their evolutionary fitness, measured in terms of past realized profits. The dynamics of our cobweb model is driven by a four-dimensional nonlinear map. We analytically show that its unique steady state may become unstable due to a Neimark-Sacker bifurcation, a scenario that gives rise to cyclical price dynamics, as observed in actual commodity markets. Simulations furthermore reveal that our cobweb model may also produce chaotic motion
Speculative behaviour and complex asset price dynamics: A global analysis
No full textThis paper analyses the dynamics of a model of a share market consisting of two groups of traders: fundamentalists, who base their trading decisions on the expectation of a return to the fundamental value of the asset, and chartists, who base their trading decisions on an analysis of past price trends. The model is reduced to a two-dimensional map whose global dynamic behaviour is analysed in detail. The dynamics are affected by parameters measuring the strength of fundamentalist demand and the speed with which chartists adjust their estimate of the trend to past price changes. The parameter space is characterized according to the local stability/instability of the equilibrium point as well as the non-invertibility of the map. The method of critical curves of non-invertible maps is used to understand and describe the range of global bifurcations that can occur. It is also shown how the knowledge of deterministic dynamics uncovered here can aid in understanding the behaviour of stochastic versions of the model. © 2002 Elsevier Science B.V. All rights reserved
Nonlinearity in Economics and Social Science: The Outstanding Contributions of John Barkley Rosser Jr
No full textThe pioneering work of John Barkley Rosser Jr. (1948–2023) in various subfields of economics emphasizes the fact that economic and social phenomena are inherently nonlinear and often discontinuous. From this standpoint, Barkley has contributed substantially to a paradigm shift in economic theory and modelling. Both his influential research work and his unceasing survey work on different approaches and schools of thought in economics and social science, carried out through the lens of complexity theory, have succeeded to develop a broader view on economic thinking and continue to inspire many researchers worldwide. The articles in this issue cover a number of research areas and themes that were central to Barkley's work, from technological progress to evolutionary competition between firms, from regional science to income inequality, from environmental economics to more general macroeconomic themes, such as bubbles and crashes, financial instabilities and policy issues
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