0000000000230894
AUTHOR
Jochen Jungeilges
Dynamics of a minimal consumer network with bi -directional influence
Abstract We study the dynamics of a model of interdependent consumer behavior defined by a family of two-dimensional noninvertible maps. This family belongs to a class of coupled logistic maps with different nonlinearity parameters and coupling terms that depend on one variable only. In our companion paper we considered the case of independent consumers as well as the case of uni-directionally connected consumers. The present paper aims at describing the dynamics in the case of a bi-directional connection. In particular, we investigate the bifurcation structure of the parameter plane associated with the strength of coupling between the consumers, focusing on the mechanisms of qualitative tr…
Sensitivity analysis of consumption cycles
We study the special case of a nonlinear stochastic consumption model taking the form of a 2-dimensional, non-invertible map with an additive stochastic component. Applying the concept of the stochastic sensitivity function and the related technique of confidence domains, we establish the conditions under which the system's complex consumption attractor is likely to become observable. It is shown that the level of noise intensities beyond which the complex consumption attractor is likely to be observed depends on the weight given to past consumption in an individual's preference adjustment.
Noise-induced transitions in a stochastic Goodwin-type business cycle model
Abstract We motivate and specify a stochastic Goodwin-type business cycle model. Our analysis focusses on a subset of the parameter space where several attractors coexist. Applying a semi-numerical approach based on the stochastic sensitivity function and confidence domains due to Milstein and Ryashko (1995) , we study random transitions between stable attractors in the context of the Goodwin-type economy embedded in an uncertain environment. Relying on a mix of analytical considerations and simulations we demonstrate that under weak noise levels regime switching is a prominent feature in the presence of low saving rates. Moreover, we explain how increased uncertainty can induce an essentia…
Asset price dynamics in a “bull and bear market”
Abstract We generalize an existing asset market model with heterogenous agents. In particular, we consider the case in which no-trade and low-trade intervals of chartists and fundamentalists respectively are not congruent. Thus we model chartist and fundamentalists who respond to asset prices in agent-specific neighborhoods around the fundamental value with different trade intensities. The resulting asset price dynamics is generated by a one-dimensional 5-piece linear map with discontinuities. Our analysis of this map focusses on coexisting price equilibria. Conditions for their existence and stability are determined analytically. By visualizing the results we allow for a basic bifurcation …
Stochastic sensitivity of bull and bear states
We study the price dynamics generated by a stochastic version of a Day–Huang type asset market model with heterogenous, interacting market participants. To facilitate the analysis, we introduce a methodology that allows us to assess the consequences of changes in uncertainty on the dynamics of an asset price process close to stable equilibria. In particular, we focus on noise-induced transitions between bull and bear states of the market under additive as well as parametric noise. Our results are obtained by combining the stochastic sensitivity function (SSF) approach, a mixture of analytical and numerical techniques, due to Mil’shtein and Ryashko (1995) with concepts and techniques from th…
Noise-induced behavioral change driven by transient chaos
We study behavioral change in the context of a stochastic, non-linear consumption model with preference adjusting, interdependent agents. Changes in long-run consumption behavior are modelled as noise induced transitions between coexisting attractors. A particular case of multistability is considered: two fixed points, whose immediate basins have smooth boundaries, coexist with a periodic attractor, with a fractal immediate basin boundary. If a trajectory leaves an immediate basin, it enters a set of complexly intertwined basins for which final state uncertainty prevails. The standard approach to predicting transition events rooted in the stochastic sensitivity function technique due to Mil…
Transitions in consumption behaviors in a peer-driven stochastic consumer network
Abstract We study transition phenomena between attractors occurring in a stochastic network of two consumers. The consumption of each individual is strongly influenced by the past consumption of the other individual, while own consumption experience only plays a marginal role. From a formal point of view we are dealing with a special case of a nonlinear stochastic consumption model taking the form of a 2-dimensional non-invertible map augmented by additive and/or parametric noise. In our investigation of the stochastic transitions we rely on a mixture of analytical and numerical techniques with a central role given to the concept of the stochastic sensitivity function and the related techni…
Empirical evaluation of home-based reablement: A review
Home-based reablement (HBR) aims to restore or increase patients’ level of functioning, thereby increasing the patients’ self-reliance and consequently decreasing their dependence on healthcare services. To date, the evidence on whether HBR is an efficient method has not been comprehensively reviewed. The aim of this study was to provide a concise summary of relevant existing findings. In addition, we provide a critical constructive assessment of the publications reflecting the extant research. The relevant literature on this topic was identified through a systematic search of appropriate databases. Thereafter, we screened the studies, first by title, followed by abstract and then by asses…