Related papers: How many more is different?
We study how environmental stochasticity influences the long-term population size in certain one- and two-species models. The difficulty is that even when one can prove that there is persistence, it is usually impossible to say anything…
The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behavior into a central question of modern science. Current models of human dynamics,…
We report numerical evidence that an epidemic-like model, which can be interpreted as the propagation of a rumor, exhibits critical behavior at a finite randomness of the underlying small-world network. The transition occurs between a…
We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in…
We propose a model coupling the classical opinion dynamics of the bounded confidence model, proposed by Deffuant et al., with an adaptive network forming a community or group structure. At each step, an individual can decide if it changes…
The emergence of nontrivial collective behavior in networks of coupled chaotic maps is investigated by means of a nonlinear mutual prediction method. The resulting prediction error is used to measure the amount of information that a local…
Quantifying human group dynamics represents a unique challenge. Unlike animals and other biological systems, humans form groups in both real (offline) and virtual (online) spaces -- from potentially dangerous street gangs populated mostly…
Many psychological experiments have subjects repeat a task to gain the statistical precision required to test quantitative theories of psychological performance. In such experiments, time-on-task can have sizable effects on performance,…
Human society and natural environment form a complex giant ecosystem, where human activities not only lead to the change of environmental states, but also react to them. By using collective-risk social dilemma game, some studies have…
The n-person Prisoner's Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be…
Tipping points have been shown to be ubiquitous, both in models and empirically in a range of physical and biological systems. The question of how tipping points cascade through systems has been less well studied and is an important one. A…
The massive amounts of data that social media generates has facilitated the study of online human behavior on a scale unimaginable a few years ago. At the same time, the much discussed apparent randomness with which people interact online…
Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…
The distribution of numbers in human documents is determined by a variety of diverse natural and human factors, whose relative significance can be evaluated by studying the numbers' frequency of occurrence. Although it has been studied…
To study the dynamics of chemical processes, we often adopt rate equations to observe the change in chemical concentrations. However, when the number of the molecules is small, the fluctuations cannot be neglected. We often study the…
Schooling fish often self-organize into a variety of collective patterns, from polarized schooling to rotational milling. Mathematical models support the emergence of these large-scale patterns from local decentralized interactions, in the…
We show that a coalescence equation exhibits a variety of critical behaviors, depending on the initial condition. This equation was introduced a few years ago to understand a toy model {studied by Derrida and Retaux to mimic} the depinning…
We study the role of noise on the nature of the transition to collective motion in dry active matter. Starting from field theories that predict a continuous transition at the deterministic level, we show that fluctuations induce a…
Bifurcation analysis has many applications in different scientific fields, such as electronics, biology, ecology, and economics. In population biology, deterministic methods of bifurcation are commonly used. In contrast, stochastic…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…