We consider a stochastic version of a 2D-discontinuous piecewise-linear map that describes the dynamics of a financial market model with heterogeneous traders, extended by the introduction of noisy signals that influence the market maker's price-setting. Using Stochastic Sensitivity Function (SSF) analysis, we examine how exogenous noise interacts with coexisting attractors in this class of maps. Three findings emerge: First, we show that the SSF does not diverge near border-collision bifurcation unlike the SSF near bifurcations associated with stability loss, revealing a structural property unique to piecewise-smooth dynamics. Second, we identify and dissect a novel noise-induced transition mechanism that operates between state-space partitions caused by the discontinuity of the map, which we formalize through the concept of d-critical intensity. Third, we demonstrate that this mechanism explains stochastic phenomena previously unaccounted for, such as unidirectional and bidirectional transitions between cycles within their basins, and the emergence of ghost dynamics. These results broaden the scope of SSF analysis, provide new insights into irregular market fluctuations under noise, and may be useful in studying other applied models in the presence of stochastic forces where the dynamics are described by discontinuous piecewise-smooth maps.

The present paper aims to further develop applicable methodology for studying the effect(s) of noise in dynamic economic settings. For that purpose we analyze a two-dimensional smooth non-invertible map modeling rational consumer choice in the presence of exogenous noise. To obtain a baseline, we first study the attractors of the deterministic system representing long-run consumption patterns, their basins of attraction and bifurcation scenarios. Here, we identify and characterize two areas of the parameter space in which extreme forms of multistability exist. In one of the parametric zones, all possible forms of attractors (fixed point, cycle, closed invariant curve, and chaotic attractor) coexist. To analyze noise-induced phenomena we use the stochastic sensitivity function technique and the confidence domain method. We describe successive multistage transitions between attractors and groups of attractors and define a dominant attractor characterizing the final state of long-run consumption behavior.

This work is devoted to the study of a map that describes the classical model of interaction between two populations of the "predator-prey" type in the presence of environmental noise. We carry out the analysis from several perspectives. First, deterministic bifurcation scenarios for attractors and their basins of attraction are studied. The critical line method is used to describe the occurrence of non-connected basins of attraction. Subsequently, we analyze the stochastic model using semi-analytical methods, namely the stochastic sensitivity function and the confidence domain method. A constructive parametric description of population extinction caused by random noise is given. An estimate of the critical noise intensity for the occurrence of the described phenomena is obtained. Finally, we provide a descriptive analysis of the extinction time series for prey and predator populations. By establishing the existence of a pronounced right-hand tail of the extinction-time density, we demonstrate that a species might avoid extinction over extended time periods.

We investigate the dynamics of household consumption in a setting in which households are connected across income classes. Low- and high-income households form preferences endogenously, conditional on their own and their neighbor’s past consumption. The modeling effort relies on a stochastic dynamic model of interdependent consumer choice in which the demand for commodities evolves according to a non-linear difference equation with stochastic initial states. The analysis targets a region of the parameter space that corresponds to salient features of a mixed-income neighborhood in which households are connected. Standard methods of asymptotic analysis of dynamic systems (e.g. bifurcation analysis) are combined with numerical simulation, statistical modelling of extreme events and statistical estimation techniques to investigate the dynamics. From the mathematical point of view, our analysis reveals the existence of intricate bifurcation pattern, coexistence of multiple attractors, complex basins and long transients. The essential economic finding states that key features of household consumption vary significantly in the influence the high-income households exert on the preference formation of the low-income households. In particular, we find that the prevalence of long transients, i.e. long waiting times before convergence to asymptotic states occur, is inversely related to the type of connectedness considered. We demonstrate that the dynamics of the consumption trajectory evolving over an extended time period before it settles on long-run simple consumption pattern, may not at all be captured by an asymptotic state. Thus, policies targeting the economies in mixed-income neighborhoods that are solely based on information about long-run consumption states, might trigger unwanted, unanticipated effects.

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'shtein and Ryashko (1995) does not apply since the required exponentially stable attractor, for which a confidence region could be constructed, does not exist. To solve the prediction problem we propose a heuristic based on the idea that a vague manifestation of a non-attracting chaotic set (chaotic repellor) - could serve as a surrogate for an attractor. A representation of the surrogate is generated via an algorithm for generating the boundary of an absorbing area due to Mira et al. (1996). Then a confidence domain for the surrogate is generated using the approach due to Bashkirtseva and Ryashko (2019). The intersections between this confidence region and the immediate basins of the coexisting attractors can then be used to make predictions about transition events. Preliminary assessments show that the heuristic indeed explains the transition probabilities observed in numerical experiments.

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 analysis in a 4-dimensional parameter space. According to our findings the extent of the disparity between the no-trade and low-intervals effects the existence of equilibria but not their stability. (c) 2020 Published by Elsevier B.V.

We study behavioral change as a transition between coexisting attractors in the context of a stochastic, non-linear consumption model with interdependent agents. Relying on the indirect approach to the analysis of a stochastic dynamic system, and employing a mix of analytical, numerical and graphical techniques, we identify conditions under which such transitions are likely to occur. The stochastic analysis depends crucially on the stochastic sensitivity function technique as it can be applied to the stochastic analoga of closed invariant curves [14], [1]. We find that in a moderate noise environment increased peer influence actually reduces the complexity of observable long-run consumer behavior.

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 assessing full-text eligibility. A checklist of 15 criteria was developed and used as the basis for the quality assessment. In total, 12 studies from Australia, New Zealand, the USA and Norway were included in the full-text review. The studies reported estimated cost differences between HBR and usual care after the intervention. All the studies indicated lower costs for HBR, but not all of them reported a significant difference. The same pattern was also found for other measures of physical functioning and quality of life. The assessment revealed one specific common pattern: None of the papers scrutinized provided sufficient information about the data or the statistics employed, and all lacked external validity. Some promising results have been reported with respect to HBR reducing the need for specialist or residential care. In short, the existing evidence regarding the effects of HBR is still inconclusive. The findings from the quality assessment should motivate a multidisciplinary approach for future research on HBR. Published: Online May 2021.

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 technique of confidence domains. We find that in the case of parametric noise the stochastic sensitivity of fixed points and cycles considered is considerably higher than in the case of additive noise. Three types of noise induced transitions between attractors are identified: (i) Escape from a stochastic fixed point with converge to a stochastic k-cycle, (ii) escape from the stochastic k-cycle to a stochastic fixed point, and (iii) cases in which the consumption process moves between the respective stochastic attractors for ever. The noise intensities at which such transitions are likely to occur tend to be smaller in the case of parametric noise than with additive noise.

Background: Home-based reablement (HBR) aims to restore or increase a patient’s level of functioning, thereby increasing the patient’s 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. Method: 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 assessing fulltext eligibility. A checklist of 15 criteria was developed and used as the basis for the quality assessment. Results: In total, 11 studies from Australia, New Zealand, the USA and Norway were included in the full-text review. The studies reported estimated cost differences between HBR and usual care after the intervention. All the studies indicated lower costs for HBR, but not all of them reported a significant difference. The same pattern was also found for other measures of physical functioning and quality of life. The assessment revealed one specific common pattern: None of the papers scrutinized provided sufficient information about the data or the statistics employed, and all lacked external validity. Conclusion: Some promising results have been reported with respect to HBR reducing the need for specialist or residential care. In short, the existing evidence regarding the effects of HBR is still inconclusive. The findings from the quality assessment should motivate a multidisciplinary approach for future research on HBR.

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.

Both the public and the academic discourse of the post-crisis era have produced most controversial views concerning adequate national savings rates. We add to this discussion by analyzing the role of the savings rate for the dynamics of an economy embedded in a turbulent environment. To this end we study the dynamics of a stochastic Goodwin-type business cycle model using a mix of analytical- and simulation techniques. Focussing on a region of the parameter space that exhibits multi-stability, we apply the stochastic sensitivity function technique and Lyapunov exponents to scrutinize the dynamics of the stochastic economic system. We find that the savings rate affects the sensitivity of the economic system, as well as the distribution of economic states. The sensitivity of the system is inversely related to the level of the savings rate. Specifically, we demonstrate that high volatility phases of the cycle vary as the savings rate is changed. For low (high) levels of the savings rate the stochastic Goodwin economy will remain relatively often in sensitive (robust) states. Our theoretical investigation suggests that strategies involving reasonably high national savings rates might help to avoid the negative welfare implications of sensitive and even chaotic income dynamics along the cycle.

In a model of interdependent consumer behavior due to (Econ Lett 27(2):145–150 1988, J Econ Behav Organ 21(2):223–231 1993) an individual adjusts his preferences in response to his own past consumption decisions and the observable past consumption of another individual. The resulting 2D non-invertible demand system exhibits a rich dynamics. We focus on two special cases: The baseline case of two independent consumers and a situation in which the autonomous individual 1 is viewed as a representative member of a group that serves as a normative reference group for individual 2. The consumption behavior of individual 2 is determined by his own past consumption experience as well as by the observable consumption behavior of individual 1, who is in turn not influenced by individual 2. The associated map belongs to the class of triangular maps. Our analysis focuses on the coexistence of attractors and the mechanisms underlying qualitative transformations of attractors. Relying on a mix of analytical, numerical, and graphical methodology, we demonstrate how various bifurcations occur as the importance of the individuals’ own past consumption as well as the strength of influence of individual 1 on 2 varies. Economic interpretations of the observed dynamic phenomena are emphasized.

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 essentially unpredictable income process out of an apparently stable high-income level situation. All dynamic phenomena are explained in terms of key concepts constituting the stochastic sensitivity function method. (C) 2017 Elsevier B.V. All rights reserved.

We develop a model with heterogeneous and socially interacting investors applying different technical trading rules (algorithms), by extending the seminal model of Day and Huang (1990). The original model consists of (sophisticated) α-investors, (unsophisticated) β-investors and a market maker. We have studied the nonlinearity features and described the dynamic behavior of the market. In the extended model, β-investors are replaced by heterogeneous and socially integrated algo-traders. Through the communication process, each investor is able to obtain information about certain other investors and his characteristics (wealth, stress indicator and trading rule). If he finds a superior investor, he will adapt his or hers algorithm. Based on ten dissimilar technical trading rules we constructed some numerical experiments, and simulated the model. Then we evaluated the mean wealth and the long run price behavior. The combination of algo-traders and the sophisticated investors resulted in price fluctuates of different types. The volatility was typically highest at the beginning of the different price series, and in one of the series a stable 10-cycle appeared. This cycle seems consistent for some levels of the flocking coefficient in the bifurcation diagram that was generated for the original Day and Huang model. The main conclusion is that unsophisticated investors does not destabilize the market. Our extended model provides several starting points for future work.

We report the results from a questionnaire-type experiment designed to elicit whether individuals decide in accordance with the equity axiom constituent for Rawls’s second principle. The experiment is sequential in nature. Hence it generates panel data. We use recently developed panel data methods for studying the role that state dependence and unobservable individual-specific effects play for the observed equity judgements. The results indicate that a dominant share of our probants initially adhere to Hammond’s equity axiom, but that many of these leave the Rawlsian position at later stages of the experiment. Although state dependence plays a significant role it cannot alone explain the observed decision behavior. Individual-specific effects are also important.

This study examines how globalization of corporate governance practices influence the risk of European CEOs being dismissed. We argue that the harsh monitoring of the American corporate governance system spills over to the rest of the world as a result of this globalization. We focus on direct and indirect American influence on the dismissal performance sensitivity among the 250 largest European publicly listed firms. The indirect influence is assumed to materialize via European firms cross-listing on U.S. exchanges, whereas the direct influence is assumed to appear as a result of European firms hiring of American independent board members. Both sources of influence are hypothesized to result in increased dismissal performance sensitivity. The empirical results show a significant increase in the dismissal sensitivity in poorly performing companies with American board membership whereas no significant increase is found from cross-listing in the U.S.

A questionnaire-type experiment was conducted in Lithuania and Norway in order to generate two samples suitable for a comparative examination of equity judgements.The results reveal large differences between the two countries. Norwegian probants had a much higher propensity to decide in accordance with Rawls’ second principle than had Lithuanian probants. Equity judgements are also strongly dependent on the context of choice. The results are interpreted within a framework describing the formation of social preferences. More specifically, differences in observed equity judgements in the two countries are related to differences in history, past experience and future prospects.

Abstract The notion of c̱onsistent e̱xpectations e̱quilibria (CEE) as propagated by Hommes/Sorger (1998) is reviewed. Focusing on their example of a chaotic CEE constructed in the context of a cobweb model, it is argued that such an equilibrium is a temporary one. Assuming that an agent-modeled as an individual, versatile in applying the basic tools of linear time-series econometrics-has learned the CEE, I analyze the duration of the time period over which the agent maintains her/his beliefs concerning the perceived law of motion (AR(1)). The analysis based on numerical simulations indicates that the use of techniques rooted in the linear paradigm is sufficient to generate convincing evidence against the underlying perceived law of motion.