Narrow Results

Similarity of opinions and memory about recent interactions are two main factors determining likelihood of social contacts. Here, we explore the Axelrod model with an extended conservativeness which incorporates not only similarity between individuals but also a preference to the last source of accepted information. The additional preference given to the last source of information increases the initial decay of the number of ideas in the system, changes the character of the phase transition between homogeneous and heterogeneous final states and could increase the number of stable regions (clusters) in the final state.

We propose a special opinion model on Internet users' social platform selections where users only view those converging platforms as tools to maintain their communications with all of their friends or partners and one may use more than one platform at the same time. We construct the time evolution differential equations, seek the fixed points, and study their attractability and repellency by analyzing those equations. Then, we verify the analytical results and observe their accuracy by numerical simulation. The conclusion shows that in any practical system described by our model, one platform will completely eliminate its competitor sooner or later, and when the average degree of the interaction network is relatively low, the laggard may have more chance to turn the tide, but when that average degree is high, that chance is extremely limited.

Building of hierarchy is inevitably associated with the constant competition for resources and attention. Here, we show how presence of two favored (leading) nodes affects properties of the network connecting individuals. In particular, we study how nodes characteristics depend on relative asymmetry between two leading nodes. It is shown that without strong and rigorous avoidance mechanism, individuals can support both dominating nodes. Slow redistribution of resources enhances this effect. Moreover, slow redistribution of resources results in development of social networks with a very limited number of layers.

In this paper, we explore the use of opinion dynamics models to examine changes in opinions of lifelong learning, and to identify groups of people for targeted intervention to improve their reception to lifelong learning. This method has a multitude of potential applications related to clustering and segmentation. Singapore’s initiative for lifelong learning, SkillsFuture, serves as a case study for the application of the technique. We first found a positive correlation between how motivated people are to learn and a negative correlation between how much people know about SkillsFuture opportunities, with respect to their reception to SkillsFuture courses. Then, we used an opinion dynamics model to model the evolution of opinions to produce clusters of people whose opinions will converge. The clusters were then grouped into three groups: those with the largest increase, largest decrease and a middle group. Further examining the covariates of the people in each cluster (e.g., age, last drawn salary, etc.), we propose organizing sharing sessions for the group with the largest increase, intervention for the group with the largest decrease, and gathering more information about the motivations of the middle group.

Collective migration of animals in a cohesive group is rendered possible by a strategic distribution of tasks among members: some track the travel route, which is time and energy-consuming, while the others follow the group by interacting among themselves. In this paper, we study a social dynamics system modeling collective migration. We consider a group of agents able to align their velocities to a global target velocity, or to follow the group via interaction with the other agents. The balance between these two attractive forces is our control for each agent, as we aim to drive the group to consensus at the target velocity. We show that the optimal control strategies in the case of final and integral costs consist of controlling the agents whose velocities are the furthest from the target one: these agents sense only the target velocity and become leaders, while the uncontrolled ones sense only the group, and become followers. Moreover, in the case of final cost, we prove an “Inactivation” principle: there exist initial conditions such that the optimal control strategy consists of letting the system evolve freely for an initial period of time, before acting with full control on the agent furthest from the target velocity.

This paper proposes a multiscale vision to human crowds which provides a consistent description at the three possible modeling scales, namely, microscopic, mesoscopic, and macroscopic. The proposed approach moves from interactions at the microscopic scale and shows how the same modeling principles lead to kinetic and hydrodynamic models. Hence, a unified framework is developed which permits to derive models at each scale using the same principles and similar parameters. This approach can be used to simulate crowd dynamics in complex environments composed of interconnected areas, where the most appropriate scale of description can be selected for each area. This offers a pathway to the development of a multiscale computational model which has the capability to optimize the granularity of the description depending on the pedestrian local flow conditions. An important feature of the modeling at each scale is that the complex interaction between emotional states of walkers and their motion is taken into account.

The first part of our paper presents a general survey on the modeling, analytic problems, and applications of the dynamics of human crowds, where the specific features of living systems are taken into account in the modeling approach. This critical analysis leads to the second part which is devoted to research perspectives on modeling, analytic problems, multiscale topics which are followed by hints towards possible achievements. Perspectives include the modeling of social dynamics, multiscale problems and a detailed study of the link between crowds and swarms modeling.

This editorial paper reviews the articles published in a special issue devoted to the application of active particle methods to the study of the collective dynamics of large systems of interacting entities in science and society. The applications presented in this special issue focus on the study of financial markets, cell dynamics in the context of cancer modeling, crowd vehicle and crowd dynamics, and classical problems in the kinetic theory of active particles and swarm theory. A critical analysis is proposed to look forward at new perspectives, with emphasis on the interaction of multiple social dynamics.

This paper presents a survey and critical analysis of the mathematical literature on modeling and simulation of human crowds taking into account behavioral dynamics. The main focus is on research papers published after the review [N. Bellomo and C. Dogbè, On the modeling of traffic and crowds: A survey of models, speculations, and perspectives, SIAM Rev. 53 (2011) 409–463], thus providing important research perspectives related to new, emerging trends. The presentation addresses the scaling problem corresponding to microscopic (individual-based), mesoscopic (kinetic), and macroscopic (hydrodynamic) modeling and analysis. A multiscale vision guides the overall content of the paper. The critical analysis of the overall content naturally leads to research perspectives. A selection of them is brought to the attention of the interested reader together with hints on how to deal with them.

This editorial paper reviews the articles published in a special issue devoted to the application of active particle methods applied to the study of the collective dynamics of large systems of interacting entities in science and society. The applications presented in this special issue focus on the study of financial markets, cell dynamics in the context of cancer modeling, vehicle and crowd vehicle and crowd dynamics, and classical problems in the kinetic theory of active particles and swarm theory. A critical analysis is proposed to look forward to research. Perspectives with emphasis on the interaction of multiple social dynamics.

Social behavior in crowds, such as herding or increased interpersonal spacing, is driven by the psychological states of pedestrians. Current macroscopic crowd models assume that these are static, limiting the ability of models to capture the complex interplay between evolving psychology and collective crowd dynamics that defines a “social crowd”. This paper introduces a novel approach by explicitly incorporating an “activity” variable into the modeling framework, which represents the evolving psychological states of pedestrians and is linked to crowd dynamics. To demonstrate the role of activity, we model pedestrian egress when this variable captures stress and awareness of contagion. In addition, to highlight the importance of dynamic changes in activity, we examine a scenario in which an unexpected incident necessitates alternative exits. These case studies demonstrate that activity plays a pivotal role in shaping crowd behavior. The proposed modeling approach thus opens avenues for more realistic macroscopic crowd descriptions with practical implications for crowd management.

A discrete in time model of ideological competition is formulated taking into account population migration. The model is based on interactions between global populations of non-believers and followers of different ideologies. The complex dynamics of the attracting manifolds is investigated. Conversion from one ideology to another by means of (i) mass media influence and (ii) interpersonal relations is considered. Moreover a different birth rate is assumed for different ideologies, the rate being assumed to be positive for the reference population, made of initially non-believers. Ideological competition can happen in one or several regions in space. In the latter case, migration of non-believers and adepts is allowed; this leads to an enrichment of the ideological dynamics. Finally, the current ideological situation in the Arab countries and China is commented upon from the point of view of the presently developed mathematical model. The massive forced conversion by Ottoman Turks in the Balkans is briefly discussed.

The modeling of small group dynamics represents a hard challenge despite the effort of disciplines such as sociophysics and social psychology. The interaction between the complex topology of human social structures/communities and the cognitive processes characterizing humans at the microscopic level, are the focus of the classical social cognition paradigm, and it has been deeply researched in the last century. In the present study we used a web based Chat room as an experimental environment for the study of social interactions within a small group of people. The target of the present study is to explore the relations between the affinity among individual and their communication dynamics. We designed three different experimental tasks (social problem), with a crescent degree of social complexity, in order to test the impact of different social constraints on the evolution of the affinity network, as well as on the dynamics of communication. Our aim is to define the "cognitive recipes" used by the subjects to solve the required social problems. Our results show that the complexity of the social problem affects the relation between affinity and communication networks, influencing at the same time both affinity and opinion. We use the sociophysics and social cognitive models in order to interpret the results, showing the limits of the most diffused sociophysics models when aiming at forecasting the dynamics of a small group.

In this work, we study the critical behavior of a three-state opinion model in the presence of noise. This noise represents the independent behavior, that plays the role of social temperature. Each agent on a regular $D$-dimensional lattice has a probability $q$ to act as independent, i.e., he can choose his opinion independent of the opinions of his neighbors. Furthermore, with the complementary probability $1-q$, the agent interacts with a randomly chosen nearest neighbor through a kinetic exchange. Our numerical results suggest that the model undergoes non-equilibrium phase transitions at critical points $q_c$ that depend on the lattice dimension. These transitions are of order–disorder type, presenting the same critical exponents of the Ising model. The results also suggest that the upper critical dimension of the model is $D_c=4$, as for the Ising model. From the social point of view, with increasing number of social connections, it is easier to observe a majority opinion in the population.

This chapter reveals the depth of the transformational nature inherent in the Mereon Matrix showing how clusters and singles of polyhedra, 33 unified forms, scale to infinity, internally and externally. This chapter suggests significant physical, psychological and sociological implications inherent in the structure and dynamics of the Matrix’s outermost polyhedron. Referred to as the Context, this geosphere iterates between 120 and 180 faces as it opens and closes, expands and contracts. Image intense, it is revealed how localised environmental energy is required, received and processed to eventually produce new systems and/or product that expands the global environment.

In this paper we propose a dynamical interpretation of the sociological distinction between large and small groups of interacting individuals. In the former case individual behaviors are largely dominated by the group effect, while in the latter mutual relationships do matter. Numerical and analytical tools are combined to substantiate our claims.