Proving chaos for a system of coupled logistic maps: A topological approach.

In the work, we prove the presence of chaotic dynamics, for suitable values of the model parameters, for the discrete-time system, composed of two coupled logistic maps, as formulated in Yousefi et al. [Discrete Dyn. Nat. Soc. 5, 161-177 (2000)], which describes two interdependent economies, characterized by two competitive markets each, with a demand link between them. In particular, we rely on the SAP (Stretching Along the Paths) method, based on a stretching relation for maps defined on sets homeomorphic to the unit square and expanding the paths along one direction. Such technique is topological in nature and allows to establish the existence of a semiconjugacy between the considered dynamical system and the Bernoulli shift, so that the main features related to the chaos of the latter (e.g., the positivity of the topological entropy) are transmitted to the former. In more detail, we apply the SAP method both to the first and to the second iterate of the map associated with our system, and we show how dealing with the second iterate, although being more demanding in terms of computations, allows for a larger freedom in the sign and in the variation range of the linking parameters for which chaos emerges. Moreover, the latter choice guarantees a good agreement with the numerical simulations, which highlight the presence of a chaotic attractor under the conditions derived for the applicability of the SAP technique to the second iterate of the map.

Rational expectations and differentiated information costs for heterogeneous fundamentalists in an evolutive Muthian cobweb model.

We extend the evolutionary cobweb setting proposed in Hommes and Wagener [J. Econ. Behav. Organ. 75, 25-39 (2010)] in which the share updating mechanism is based on a comparison among the profits realized by the different kinds of agents, by assuming that the market is populated by rational producers, endowed with perfect foresight expectations about prices, in addition to biased and unbiased fundamentalists. Moreover, we suppose that agents face heterogeneous information costs, which are proportional to their rationality degree. Since we found in Naimzada and Pireddu [Econ. Lett. 186, 108513 (2020a)] that considering diversified information costs for fundamentalists shrinks the stability region of the steady state, while we discovered in Naimzada and Pireddu [J. Econ. Behav. Organ. 177, 415-432 (2020b)] that introducing rational agents enlarges it, we analyze whether one of the two aspects always prevails over the other one when they are jointly taken into account. We also investigate if the chaotic phenomena detected in Naimzada and Pireddu [J. Econ. Behav. Organ. 177, 415-432 (2020b)] emerging when enriching the original framework in Hommes and Wagener [J. Econ. Behav. Organ. 75, 25-39 (2010)] with rational agents, persist or are inhibited by the introduction of information costs for all agent types. We complete our analysis by studying the network of the relationships among the four settings obtained possibly considering information costs for biased and unbiased fundamentalists and possibly introducing rational agents.

Agents' beliefs and economic regimes polarization in interacting markets.

In the present paper, a model of a market consisting of real and financial interacting sectors is studied. Agents populating the stock market are assumed to be not able to observe the true underlying fundamental, and their beliefs are biased by either optimism or pessimism. Depending on the relevance they give to beliefs, they select the best performing strategy in an evolutionary perspective. The real side of the economy is described within a multiplier-accelerator framework with a nonlinear, bounded investment function. We study the effect of market integration, in particular, of the financialization of the real market. We show that strongly polarized beliefs in an evolutionary framework can introduce multiplicity of steady states, which, consisting in enhanced or depressed levels of income, reflect and reproduce the optimistic or pessimistic nature of the agents' beliefs. The polarization of these steady states, which coexist with an unbiased steady state, positively depends on that of the beliefs and on their relevance. Moreover, with a mixture of analytical and numerical tools, we show that such static characterization is inherited also at the dynamical level, with possibly complex attractors that are characterized by endogenously fluctuating pessimistic and optimistic prices and levels of national income, with the effect of having several coexisting business cycles. This framework, when stochastic perturbations are included, is able to account for stylized facts commonly observed in real financial markets, such as fat tails and excess volatility in the returns distributions, as well as bubbles and crashes for stock prices.

Fashion cycle dynamics in a model with endogenous discrete evolution of heterogeneous preferences.

We propose a discrete-time exchange economy evolutionary model, in which two groups of agents are characterized by different preference structures. The reproduction level of a group is related to its attractiveness degree, which depends on the social visibility level, determined by the consumption choices of the agents in that group. The attractiveness of a group is initially increasing with its visibility level, but it becomes decreasing when its visibility exceeds a given threshold value, due to a congestion effect. Thanks to the combined action of the price mechanism and of the share updating rule, the model is able to reproduce the recurrent dynamic behavior typical of the fashion cycle, presenting booms and busts both in the agents' consumption choices and in the population shares. More precisely, we investigate the existence of equilibria and their stability, and we perform a qualitative bifurcation analysis on varying the parameter describing the group's heterogeneity degree. From a global viewpoint, we detect, among others, multistability phenomena in which the group coexistence is dynamic, either regular or irregular, and the fashion cycle occurs. The existence of complex dynamics is proven via the method of the turbulent maps, working with homoclinic orbits. Finally, we provide a social and economic interpretation of the main scenarios.

Real and financial market interactions in a multiplier-accelerator model: Nonlinear dynamics, multistability and stylized facts.

In the present paper, we investigate the dynamics of a model in which the real part of the economy, described within a multiplier-accelerator framework, interacts with a financial market with heterogeneous speculators, in order to study the channels through which the two sectors influence each other. Employing analytical and numerical tools, we investigate stability conditions as well as bifurcations and possible periodic, quasi-periodic, and chaotic dynamics, enlightening how the degree of market interaction, together with the accelerator parameter and the intervention of the fiscal authority, may affect the business cycle and the course of the financial market. In particular, we show that even if the steady state is locally stable, multistability phenomena can occur, with several and complex dynamic structures coexisting with the steady state. Finally, simulations reveal that the proposed model is able to explain several statistical properties and stylized facts observed in real financial markets, including persistent high volatility, fat-tailed return distributions, volatility clustering, and positive autocorrelation of absolute returns.

Hyaline vascular Castleman's disease of the mediastinum.

Castleman's disease is rare and can be present in many sites and with a variety of symptoms. Surgery is always recommended for localized lesions to remove the mass as completely as possible, reserving other treatment modalities for unresectable cases.