Models Of Collective Behavior Research Articles

Fission-fusion dynamics and group-size-dependent composition in heterogeneous populations.

Many animal groups are heterogeneous and may even consist of individuals of different species, called mixed-species flocks. Mathematical and computational models of collective animal movement behavior, however, typically assume that groups and populations consist of identical individuals. In this paper, using the mathematical framework of the coagulation-fragmentation process, we develop and analyze a model of merge and split group dynamics, also called fission-fusion dynamics, for heterogeneous populations that contain two types (or species) of individuals. We assume that more heterogeneous groups experience higher split rates than homogeneous groups, forming two daughter groups whose compositions are drawn uniformly from all possible partitions. We analytically derive a master equation for group size and compositions and find mean-field steady-state solutions. We predict that there is a critical group size below which groups are more likely to be homogeneous and contain the abundant type or species. Despite the propensity of heterogeneous groups to split at higher rates, we find that groups are more likely to be heterogeneous but only above the critical group size. Monte Carlo simulation of the model show excellent agreement with these analytical model results. Thus, our model makes a testable prediction that composition of flocks are group-size-dependent and do not merely reflect the population level heterogeneity. We discuss the implications of our results to empirical studies on flocking systems.

Collective Behaviors Through Social Interactions in Bird Flocks

Collective behaviors in multi-agent systems (MASs) is one of the most ubiquitous phenomena in the natural world, which often exhibit through social interactions among their agents. It is very important to understand the theoretical mechanisms at the basis of different collective behaviors. Therefore, various techniques and methods have been developed and investigated against this issue over the last decades. In this paper, we concentrate on several models of collective behaviors in bird flocks, a representative kind of MAS. Moreover, this article aims at providing a discussion of various facets of this interdisciplinary field, including simulation models, mathematical methods and control theory. The purposes are to offer readers a better understanding of complex systems and to promote this emerging topic on MASs.

Construction Management, Construction Method and System, Optimization and Innovation in Structural Design

In recent years, a number of studies have successfully transformed various models for biological collective behavior into intelligent optimization algorithms. These bio-inspired optimization techniques have been developed to provide better solutions than traditional methods to a variety of engineering problems. This paper attempts to apply and compare recent bio-inspired algorithms for determining the best layout of construction temporary facilities. To validate the performance of the proposed techniques, an actual building construction project was used as a test problem. Based on the obtained results, the performance of each bio-inspired algorithm is highlighted and discussed. This paper presents beneficial insights to decision-makers in the construction industry that are involved in handling optimization problems.

Anti-Conformism in the threshold Model of Collective Behavior

We provide a first study of the threshold model, where both conformist and anti-conformist agents coexist. The paper is in the line of a previous work by the first author (Grabisch et al., 2018), whose results will be used at some point in the present paper. Our study bears essentially in answering the following question: Given a society of agents with a certain topology of the network linking these agents, given a mechanism of influence for each agent, how the behavior/opinion of the agents will evolve with time, and in particular can it be expected that it converges to some stable situation, and in this case, which one? Also, we are interested by the existence of cascade effects, as this may constitute a undesirable phenomenon in collective behavior. We divide our study into two parts. In the first one, we basically study the threshold model supposing a fixed complete network, where every one is connected to every one, like in the work of Granovetter (1978). We study the case of a uniform distribution of the threshold, of a Gaussian distribution, and finally give a result for arbitrary distributions, supposing there is one type of anti-conformist. In a second part, the graph is no more complete and we suppose that the neighborhood of an agent is random, drawn at each time step from a distribution. We distinguish the case where the degree (number of links) of an agent is fixed, and where there is an arbitrary degree distribution.

On long-time asymptotics for viscous hydrodynamic models of collective behavior with damping and nonlocal interactions

Hydrodynamic systems arising in swarming modeling include nonlocal forces in the form of attractive–repulsive potentials as well as pressure terms modeling strong local repulsion. We focus on the case where there is a balance between nonlocal attraction and local pressure in presence of confinement in the whole space. Under suitable assumptions on the potentials and the pressure functions, we show the global existence of weak solutions for the hydrodynamic model with viscosity and linear damping. By introducing linear damping in the system, we ensure the existence and uniqueness of stationary solutions with compactly supported density, fixed mass and center of mass. The associated velocity field is zero in the support of the density. Moreover, we show that global weak solutions converge for large times to the set of these stationary solutions in a suitable sense. In particular cases, we can identify the limiting density uniquely as the global minimizer of the free energy with the right mass and center of mass.

Particle Based gPC Methods for Mean-Field Models of Swarming with Uncertainty

In this work we focus on the construction of numerical schemes for the approximation of stochastic mean--field equations which preserve the nonnegativity of the solution. The method here developed makes use of a mean-field Monte Carlo method in the physical variables combined with a generalized Polynomial Chaos (gPC) expansion in the random space. In contrast to a direct application of stochastic-Galerkin methods, which are highly accurate but lead to the loss of positivity, the proposed schemes are capable to achieve high accuracy in the random space without loosing nonnegativity of the solution. Several applications of the schemes to mean-field models of collective behavior are reported.

Culture in the Digital Civilization: A New Stage in Understanding the Future Strategy for Sustainable Development

The current situation is determined by a plurality of uncertainties of social, economic, environmental and technological nature, which cause instability of development and form a new stage of social development conventionally called digital civi­lization. The ambiguity of interpretation of this term is also reflected in its derivatives, and this fully applies to the concept of digital economy.Development of the digital infrastructure, transition to the network principles of communication, and personalization of the Internet, are the factors that change the ethical principles and foundations of social and cultural interaction. The issue of individual and collective cultural practices and behavior models based on the new hierarchy of values is of particular relevance in social and humanitarian knowledge. In the information society, the dramatization of trust and the vulnerability of freedom testify to the society’s transition to a new quality — “normal anomie”.Basing on the analysis of scientific projects, documents, some forecasts and development scenarios of the digital economy and its social consequences, this study aims to trace the reflection of the relationship between the digital economy and culture, and to identify the ways that reflect the inclusion of culture in digital economy development programs. In this case, culture can be considered in the context of these programs as an element of infrastructure, and an institutional contour, representing a part of human and technological capital.The authors’ ideas are concentrated around the search for the grounds of the transformational changes taking place in scientific research, educational and cultural practices that have potential to form a sustainable cultural context of the digital civilization, which will be supported in order to prevent the pressure of the processes generated by technology that lead to “dehumanization” of development.The applied part of the study reveals one aspect of “digital culture” — its ability to saturate network multimedia spaces with meanings and values. This increases the requirements for the quality of information on open national cultural resources — websites of libraries, cultural and recreational centers, museums, departmental portals.The article pays special attention to the analysis of consistency of the tasks on scientific-technical and technological “breakthrough” with the humanistic values of development at the initial stage of implementation of the project of “digital economy of Russia”. These transformations require community to formulate a clear and intelligible position on the humanistic imperative of developing the digital economy and digital civilization in Russia and the world. At this stage, it is still possible to identify what kind of adjustment this project needs, partial or thorough, in order to avoid ending up in a situation of value-semantic chaos, losing the main thing — socio-cultural human component of the next stage of epochal changes. There is a need for a public examination of the Digital Economy Development Program in Russia, and more coordinated, targeted civil society activities to preserve cultural and human capital.

Information Flow in a Boolean Network Model of Collective Behavior

In animal groups, leaders have often been proposed to be those individuals who possess additional knowledge about their surroundings, such as the location of a food source or a potential predator. Understanding how this information propagates through the group to shape collective response is an important step to elucidate the evolutionary basis of leadership. In this paper, we study a Boolean model of collective behavior, in which a single leader interacts with a group of followers in a binary decision-making process. Through an analytical treatment of the associated Markov chain, we establish closed-form solutions for the transition probability matrix and the stationary distribution, as functions of the noise in the decision-making process and the size of the group. We leverage these expressions to quantify information transfer within the group, measured through the information-theoretic construct of transfer entropy. We find that information transfer depends nonlinearly on the group size and noise. For low noise intensities, the system is nearly deterministic, such that no information is shared within the group; an equivalent effect is observed for large noise intensities, which mask the information transfer. We determine the existence of critical noise intensities at which the leader maximizes information transfer to a follower or followers maximize information sharing between each other for a given group size. These analytical findings suggest that noise might have a positive role in collective behavior, facilitating the transfer of knowledge within the group, from leaders to followers.

Collective behavior models with vision geometrical constraints: Truncated noises and propagation of chaos

We consider large systems of stochastic interacting particles through discontinuous kernels which has vision geometrical constrains. We rigorously derive a Vlasov–Fokker–Planck type of kinetic mean-field equation from the corresponding stochastic integral inclusion system. More specifically, we construct a global-in-time weak solution to the stochastic integral inclusion system and derive the kinetic equation with the discontinuous kernels and the inhomogeneous noise strength by employing the 1-Wasserstein distance.

Modeling Individual and Group Evacuation Decisions During Wildfires

Quantifying factors that affect evacuation decision making remains a challenging task. Progress is crucial for developing predictive models of collective behavior and for designing effective policies to guide the action of populations during wildfires. We conduct a controlled behavioral experiment to probe factors influencing evacuation decision making in the face of an impending virtual wildfire. We consider competing factors that influence small groups and the community as a whole. Based on our data, we develop two distinct but complementary empirically-driven approaches to characterize individual and group evacuation decision making. Our first approach is a stochastic model that predicts evacuation of a population of individuals guided by the same decision-making strategy, which we define to be a continuous function of key experimental variables such as the likelihood of the disaster and the availability of resources. We extend this model to investigate strategy shifts leading to differences between individual and group behavior which manifest at the collective level. In our second approach, we characterize decision making of individuals and groups by incorporating variation in individual traits, group decision protocols, and time-dependent changes in experimental variables with logistic regression. By including personal identifying characteristics of each subject, we develop a model that can predict evacuation decision times with 85.0% accuracy. In parallel, we demonstrate that the social media activity of individual subjects, specifically their Facebook use, can be used to generate an alternative individual personality profile that leads to comparable prediction accuracy of 84.2%. Our results from both approaches demonstrate the importance of using a rate-based rather than threshold function to describe individual behavior, and of accounting for social influence and individual heterogeneity in modeling group decision making.

Mean-field limit for collective behavior models with sharp sensitivity regions

We rigorously show the mean-field limit for a large class of swarming individual based models with local sharp sensitivity regions. For instance, these models include nonlocal repulsive-attractive forces locally averaged over sharp vision cones and Cucker-Smale interactions with discontinuous communication weights. We construct global-in-time defined notion of solutions through a differential inclusion system corresponding to the particle descriptions. We estimate the error between the solutions to the differential inclusion system and weak solutions to the expected limiting kinetic equation by employing tools from optimal transport theory. Quantitative bounds on the expansion of the 1-Wasserstein distance along flows based on a weak-strong stability estimate are obtained. We also provide different examples of realistic sensitivity sets satisfying the assumptions of our main results.

Global Existence and Stability of Nearly Aligned Flocks

We study regularity of a hydrodynamic singular model of collective behavior introduced in \cite{ST1}. In this note we address the question of global well-posedness in multi-dimensional settings. It is shown that any initial data $(u,\rho)$ with small velocity variations $|u(x) - u(y)| < \e$ relative to its higher order norms, gives rise to a unique global regular solution which aligns and flocks exponentially fast. Moreover, we prove that the limiting flocks are stable.

Modeling and intelligent optimization of social collective behavior with online public opinion synchronization

Today, the public opinion synchronization on the network platform is becoming one of important issues worthy of careful study. In this paper, we take synchronization evolution phenomenon as an objective and adopt artificial bee colony (ABC) to evaluate network synchronization effects with optimization theory to find out an appropriate network structure. Firstly, we use the Kuramoto oscillators as a metaphor of the social system collective behavior. Secondly, combined with the social network characteristics obtained from the data of Sina Micro-Blog, a synchronization evolution model of Internet public opinion based on Kuramoto one is established. Subsequently, evolutionary multi-objective optimization model is set up and the ABC method is used to optimize the level of network synchronization, the synchronization starting time and the cost of public opinion synchronization. Finally, case analysis on “Double Eleven” Internet Marketing as well as Cadmium Poisoned Rice Event demonstrates that the synchronization performance of weak coupled system can be enhanced by offering reasonable configuration of the connection cost and the synchronization duration cost. In addition, a certain degree of increase in input cost can promote the synchronization performance and extend the synchronization duration significantly.

Direction-dependent interaction rules enrich pattern formation in an individual-based model of collective behavior.

Direction-dependent interaction rules are incorporated into a one-dimensional discrete-time stochastic individual-based model (IBM) of collective behavior to compare pattern formation with an existing partial differential equation (PDE) model. The IBM is formulated in terms of three social interaction forces: repulsion, alignment, and attraction, and includes information regarding conspecifics’ direction of travel. The IBM produces a variety of spatial patterns which qualitatively match patterns observed in a PDE model. The addition of direction-dependent interaction rules exemplifies how directional information transfer within a group of individuals can result in enriched pattern formation. Our individual-based modelling framework reveals the influence that direction-dependent interaction rules such as biological communication can have upon individual movement trajectories and how these trajectories combine to form group patterns.

Continuous-Time Granovetter Model

In this paper, the model of collective conformity behavior proposed in [6] and originally motivated by M. Granovetter [7] is investigated. The probabilistic foundations of the model are considered at the micro level. The model properties are studied in the case when the number of agents tends to infinity, with derivation of the transfer equation. Finally, it is established that the system trajectories coincide with the ones of an isolated Hamiltonian system.

A mean-field game model for homogeneous flocking.

Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering, and finance. We formulate and study a mean-field game model whose behavior mimics an empirically derived nonlocal homogeneous flocking model for agents with gradient self-propulsion dynamics. The mean-field game framework provides a non-cooperative optimal control description of the behavior of a population of agents in a distributed setting. In this description, each agent's state is driven by optimally controlled dynamics that result in a Nash equilibrium between itself and the population. The optimal control is computed by minimizing a cost that depends only on its own state and a mean-field term. The agent distribution in phase space evolves under the optimal feedback control policy. We exploit the low-rank perturbative nature of the nonlocal term in the forward-backward system of equations governing the state and control distributions and provide a closed-loop linear stability analysis demonstrating that our model exhibits bifurcations similar to those found in the empirical model. The present work is a step towards developing a set of tools for systematic analysis, and eventually design, of collective behavior of non-cooperative dynamic agents via an inverse modeling approach.

Collective gradient sensing in fish schools

Throughout the animal kingdom, animals frequently benefit from living in groups. Models of collective behaviour show that simple local interactions are sufficient to generate group morphologies found in nature (swarms, flocks and mills). However, individuals also interact with the complex noisy environment in which they live. In this work, we experimentally investigate the group performance in navigating a noisy light gradient of two unrelated freshwater species: golden shiners (Notemigonuscrysoleucas) and rummy nose tetra (Hemigrammus bleheri). We find that tetras outperform shiners due to their innate individual ability to sense the environmental gradient. Using numerical simulations, we examine how group performance depends on the relative weight of social and environmental information. Our results highlight the importance of balancing of social and environmental information to promote optimal group morphologies and performance.

Model of Collective Fish Behavior with Hydrodynamic Interactions.

Fish schooling is often modeled with self-propelled particles subject to phenomenological behavioral rules. Although fish are known to sense and exploit flow features, these models usually neglect hydrodynamics. Here, we propose a novel model that couples behavioral rules with far-field hydrodynamic interactions. We show that (1)a new "collective turning" phase emerges, (2)on average, individuals swim faster thanks to the fluid, and (3)the flow enhances behavioral noise. The results of this model suggest that hydrodynamic effects should be considered to fully understand the collective dynamics of fish.

The Phenomenon of Related Dynamics in Global Finances (Russia, Brazil)

The article establishes stable codependencies between international financial markets and their underlying cause and effect mechanisms, as an object of a global transformation. We demonstrate an intense co-integration between the financial markets of Russia, Brazil and the other emerging markets of Latin America (through the lens of stock markets and national currencies). The cause and effect mechanisms of this dependency are examined. We characterize the countries as analogous substitutes for investors (abundant similarities include: models of collective behaviour, ideology, model and structure of the economy, model of the financial sector, highly speculative markets in shares and currencies). The article explains an extremely limited role of the internal (primarily retail) investors in determining dynamics of the financial market. The central role of non-resident actors (global financial institutions and institutional investors) in the dynamics of the markets of Russian and Brazil is established. We demonstrate that for Russia and Brazil sources of foreign portfolio investments coincide. This includes Anglo-Saxon centers, specifically the US and British offshore jurisdictions, and the global centers of secondary importance (the Netherlands and Luxembourg). The decision making models of global investors in Russian and Brazil are examined: stock prices are driven by the oil prices, and in part by the US stock market, and rouble and real exchange rates follows oil prices and the EUR-USD currency pair. Analysis and conclusions made in the article are supported by a significant volume of statistical modelling.

Probabilistic models of individual and collective animal behavior

Recent developments in automated tracking allow uninterrupted, high-resolution recording of animal trajectories, sometimes coupled with the identification of stereotyped changes of body pose or other behaviors of interest. Analysis and interpretation of such data represents a challenge: the timing of animal behaviors may be stochastic and modulated by kinematic variables, by the interaction with the environment or with the conspecifics within the animal group, and dependent on internal cognitive or behavioral state of the individual. Existing models for collective motion typically fail to incorporate the discrete, stochastic, and internal-state-dependent aspects of behavior, while models focusing on individual animal behavior typically ignore the spatial aspects of the problem. Here we propose a probabilistic modeling framework to address this gap. Each animal can switch stochastically between different behavioral states, with each state resulting in a possibly different law of motion through space. Switching rates for behavioral transitions can depend in a very general way, which we seek to identify from data, on the effects of the environment as well as the interaction between the animals. We represent the switching dynamics as a Generalized Linear Model and show that: (i) forward simulation of multiple interacting animals is possible using a variant of the Gillespie’s Stochastic Simulation Algorithm; (ii) formulated properly, the maximum likelihood inference of switching rate functions is tractably solvable by gradient descent; (iii) model selection can be used to identify factors that modulate behavioral state switching and to appropriately adjust model complexity to data. To illustrate our framework, we apply it to two synthetic models of animal motion and to real zebrafish tracking data.