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.

Serum lipid levels during interferon therapy in patients with chronic hepatitis C.

Interferon-alpha (IFN-alpha) may affect lipid metabolism by stimulating hepatic fatty acid synthesis. The aim of this study was to evaluate serum lipid levels during IFN-alpha therapy in patients with biopsy-proven chronic active hepatitis C. A total of 22 patients (18 males and 4 females; age 25-55 years) received 3 MU of recombinant IFN-alpha 2b 3 times a week for 6 months. Serum lipids were determined at baseline and then every month until the end of therapy. All patients had normal serum lipid levels at baseline. No significant level of modification occurred in patients during the therapy. An increase in serum lipid levels during low-dose IFN-alpha therapy seems to be uncommon in hepatitis C virus-infected patients with baseline normal levels.

Detection of anti-HCV IgM antibodies in patients with chronic hepatitis C treated with interferon.

OBJECTIVE: To assess the role of IgM antibodies to hepatitis C virus core protein (anti-HCV IgM) as a marker of chronic HCV infection and as a predictor of successful interferon (IFN) treatment. DESIGN: Anti-HCV IgM levels were evaluated at baseline, during IFN therapy and during a follow-up period. METHODS: Anti-HCV IgM levels were evaluated in 62 patients (47 men and 15 women, aged 25-65 years) with biopsy-proven chronic active hepatitis C. Fifty-one of the patients received alpha-IFN 3 MU three times a week for 6 months and 11 received the same therapy for 12 months. Twenty patients showed a long-term response; fourteen responded but subsequently suffered a relapse; twenty-eight did not respond to the treatment. Follow-up in all patients lasted for at least 6 (mean +/- SD 9.8 +/- 5.4, range 6-29) months after the end of the therapy. RESULTS: Anti-HCV IgM were detected in 35 patients (56.4%) at baseline; no significant differences were observed between the three groups studied. Almost all members of the groups showing a relapse or no response remained positive at the end of therapy and follow-up. In contrast, we observed a progressive disappearance of anti-HCV IgM in patients responsive to interferon therapy over the long term. CONCLUSION: The loss of anti-HCV IgM positivity in patients positive at baseline can predict the long-term response to IFN therapy.

Caffeine clearance in subjects with constitutional unconjugated hyperbilirubinemia.

To investigate the behaviour of caffeine (CAF) in patients with Gilbert's Syndrome (GS), a combined oral loading test of caffeine and chenodeoxycholic acid was performed in 14 healthy subjects and 71 patients with GS. Indocyanine green (ICG) kinetics was tested in 50 subjects with GS and in all control subjects. Fasting serum bile acids (SBA) and clearance after CDCA loading were within normal range in normal and GS subjects. No significant difference in levels either of bilirubin or of SBA was observed in GS cases with normal (52 cases, 488 +/- 63 ml/min) or impaired (19 cases, 338 +/- 30 ml/min) caffeine clearance. Eleven GS cases showed altered ICG clearance. No correlation was found between bilirubin and bile acids, CAF or ICG. Fasting SBA were normal even in cases of CAF or ICG altered kinetics, thus excluding structural damage in unconjugated hyperbilirubinemia. CAF altered kinetics in 27% of GS cases may suggest multiple deficits in the hepatocellular metabolism, thus confirming the heterogeneity of this syndrome.