Narrow Results

The Social Percolation model recently proposed by Solomon et al. is studied on the Ising correlated inhomogeneous network. The dynamics in this is studied so as to understand the role of correlations in the social structure. Thus, the possible role of the structural social connectivity is examined.

We propose an opinion dynamics model to study the effects of heterogeneous influence of individuals on the global consensus. Each individual is assigned a weight that is proportional to the power of its degree, where the power exponent α is an adjustable parameter. Interestingly, it is found that there exists an optimal value of α leading to the shortest consensus time for scale-free networks, random networks and small-world networks. Other quantities, such as the probability that an individual's initial opinion becomes the final opinion as a function of degree, the evolution of the number of opinion clusters, as well as the relationship between average consensus time and the network size, are also studied. Our results are helpful for understanding the role of heterogeneous influence in the opinion dynamics.

We consider a dynamic group composed with a constant number of people and the people will change periodically. Every member in the community owns a value of confidence — a mechanism that measures the agent’s coherence to his or her own attitude. Based on Cellular Automata, the opinions of all agents are synchronously updated. As long as the updating frequency and updating proportion are appropriate, the open system can reach a democracy-like steady state. The majority of agents in the community will hold the same opinion.

In this work, we study a model of tax evasion. We considered a fixed population divided in three compartments, namely honest tax payers, tax evaders and a third class between the mentioned two, which we call susceptibles to become evaders. The transitions among those compartments are ruled by probabilities, similarly to a model of epidemic spreading. These probabilities model social interactions among the individuals, as well as the government’s fiscalization. We simulate the model on fully-connected graphs, as well as on scale-free and random complex networks. For the fully-connected and random graph cases, we observe that the emergence of tax evaders in the population is associated with an active-absorbing nonequilibrium phase transition, that is absent in scale-free networks.

The world evolution of the severe acute respiratory syndrome coronavirus 2 (SARS-Cov2 or simply COVID-19) led the World Health Organization to declare it a pandemic. The disease appeared in China in December 2019, and it has spread fast around the world, especially in European countries like Italy and Spain. The first reported case in Brazil was recorded in February 26, and after that the number of cases grew fast. In order to slow down the initial growth of the disease through the country, confirmed positive cases were isolated to not transmit the disease. To better understand the early evolution of COVID-19 in Brazil, we apply a Susceptible–Infectious–Quarantined–Recovered (SIQR) model to the analysis of data from the Brazilian Department of Health, obtained from February 26, 2020 through March 25, 2020. Based on analytical and numerical results, as well on the data, the basic reproduction number is estimated to $R_0=5.25$. In addition, we estimate that the ratio between unidentified infectious individuals and confirmed cases at the beginning of the epidemic is about 10, in agreement with previous studies. We also estimated the epidemic doubling time to be $2.72$ days.

The city of Rio de Janeiro is one of the biggest cities in Brazil. Drug gangs and paramilitary groups called milícias control some regions of the city where the government is not present, specially in the slums. Due to the characteristics of such two distinct groups, it was observed that the evolution of COVID-19 is different in those two regions, in comparison with the regions controlled by the government. In order to understand qualitatively those observations, we divided the city in three regions controlled by the government, by the drug gangs and by the milícias, respectively, and we consider a Susceptible-Infected-Recovered-Dead (SIRD)-like epidemic model where the three regions are coupled. Considering different levels of exposure, the model is capable to reproduce qualitatively the distinct evolution of the COVID-19 disease in the three regions, suggesting that the organized crime shapes the COVID-19 evolution in the city of Rio de Janeiro. This case study suggests that the model can be used in general for any metropolitan region with groups of people that can be categorized by their level of exposure.

In this work, we study a dynamics of tax evasion. We considered a fully-connected population divided in three compartments, namely honest tax payers, tax evaders and susceptibles, a class that is composed by honest tax payers that can become evaders. We consider a contagion model where the transitions among the compartments are governed by probabilities. Such probabilities represent the possible interactions among the individuals, as well as the government fiscalization. We show by analytical and numerical calculations that the emergence of tax evaders in the population is associated with an active-absorbing nonequilibrium first-order phase transition. In the absorbing phase, only honest tax payers survive in the steady states of the model, and we observe a coexistence of the three subpopulations in the active phase.

We use the logistic equation to model the dynamics of the GDP and the trade of the six countries with the highest GDP in the world, namely, USA, China, Japan, Germany, UK and India. From the modeling of the economic data, which are made available by the World Bank, we predict the maximum values of the growth of GDP and trade, as well as the duration over which exponential growth can be sustained. We set up the correlated growth of GDP and trade as the phase solutions of an autonomous second-order dynamical system. GDP and trade are related to each other by a power law, whose exponent seems to differentiate the six national economies into two types. Under conducive conditions for economic growth, our conclusions have general validity.

In this work, we study a simple mathematical model to analyze the emergence and control of radicalization phenomena. The population consists of core and sensitive subpopulations, and their ways of life may be at least partially incompatible. In such a case, if a conflict exists, core agents act as inflexible individuals about the issue. On the other hand, the sensitive agents choose between two options: live peacefully with core population, or oppose it. This kind of modeling was recently considered by Galam and Javarone (2016) with constant pairwise couplings. Here, we consider the more general case with time-dependent transition rates, with the aim of study the impact of such time dependence on the critical behavior of the model. The analytical and numerical results show that the nonequilibrium active-absorbing phase transition can be suppressed in some cases, with the destruction of the absorbing phase where the radical agents disappear of the population in the stationary states.

In this work, we study a simple mathematical model to analyze the emergence and control of radicalization phenomena, motivated by the recent far-right extremist events in Brazil, occurred in 8 January 2023. For this purpose, we considered a compartmental SIS-like model that takes into account only the right electors, for simplicity. The model considers radical and moderated right electors, and the transitions between the two compartments are ruled by probabilities, taking into account pairwise social interactions and the important influence of social media through the dissemination of fake news. The role of the Brazilian Federal Supreme Court on the control of such violent activities is also considered in a simple way. The analytical and numerical results show that the influence of social media is essential for the spreading and prevalence of radicalism in the population. In the presence of such social media, we show that radicalism can be controlled, but not extincted, by an external influence, that models the acting of the Federal Supreme Court over the violent activities of radicals. If the social media effect is absent, the radicalism can disappear of the population, and this phenomenon is associated with an active-absorbing nonequilibrium phase transition, like the one that occurs in the standard SIS model.

In this work we propose a simple model for the emergence of drug dealers. For this purpose, we built a compartmental model considering four subpopulations, namely susceptibles, passive supporters, drug dealers and arrested drug dealers. The target is to study the influence of the passive supporters on the long-time prevalence of drug dealers. Passive supporters are people who are passively consenting to the drug trafficking cause. First we consider the model on a fully connected network, in such a way that we can write a rate equation for each subpopulation. Our analytical and numerical results show that the emergence of drug dealers is a consequence of the rapid increase in the number of passive supporters. Such increase is associated with a nonequilibrium active-absorbing phase transition. After that, we consider the model on a two-dimensional square lattice, in order to compare the results in the presence of a simple social network with the previous results. The Monte Carlo simulation results suggest a similar behavior in comparison with the fully connected network case, but the location of the critical point of the transition is distinct, due to the neighbors’ correlations introduced by the presence of the lattice.

We present particle-based simulations for the flocking behavior of self-propelling particles. Built upon previous models, our models include realistic but simple rules for the self-propelling, drag, and inter-particle interactions. Depending on both the strength and range of the interactions, a host of stationary phases appear, including independent wandering, formation flight, swarm, and rotating vortex. Of particular interest, we determine that the rotating flock can only arise in the absence of long-range alignment. We also construct a phenomenological continuum model and obtain steady-state solutions for the rotating state.

By incorporating multi-community attachments into the continuous opinion formation model, we investigate the driving force for reaching consensus in networked systems. A phase transition from fragmentation to consensus is determined by the multiplex network structures and the coupling of different communities. A moderate number of layers and weak coupling are beneficial for consensus. The evolutionary dynamics in the present model is governed by the prolonged evolutionary time, which results from the disparities of individual opinions in different communities. Increasing the multiple layers is similar to promoting coupling between different communities. A functional relation between the convergence time and the coupling coefficient is found.

The growth of the nominal Gross Domestic Product (GDP) of national economies is modeled by the logistic function. Applying it on the GDP data of the World Bank till the year 2020, we forecast the outcome of the competitive GDP growth of Japan, Germany, the UK and India, all of whose current GDPs are very close to one another. Fulfilling one of the predictions, the GDP of India overtook the GDP of the UK in 2022. We further forecast that in 2047 the GDP of India will exceed the GDPs of both Japan and Germany. When trade saturates, large and populous countries (like India) have the benefit of high domestic consumption to propel their GDP growth.