Models Of Collective Behavior Research Articles

Reduced Variance Random Batch Methods for Nonlocal PDEs

Random Batch Methods (RBM) for mean-field interacting particle systems enable the reduction of the quadratic computational cost associated with particle interactions to a near-linear cost. The essence of these algorithms lies in the random partitioning of the particle ensemble into smaller batches at each time step. The interaction of each particle within these batches is then evolved until the subsequent time step. This approach effectively decreases the computational cost by an order of magnitude while increasing the amount of fluctuations due to the random partitioning. In this work, we propose a variance reduction technique for RBM applied to nonlocal PDEs of Fokker-Planck type based on a control variate strategy. The core idea is to construct a surrogate model that can be computed on the full set of particles at a linear cost while maintaining enough correlations with the original particle dynamics. Examples from models of collective behavior in opinion spreading and swarming dynamics demonstrate the great potential of the present approach.

Modeling fashion as an emergent collective behavior of bored individuals

Boredom is an aversive mental state that is typically evoked by monotony and drives individuals to seek novel information. Despite this effect on individual behavior, the consequences of boredom for collective behavior remain elusive. Here, we introduce an agent-based model of collective fashion behavior in which simplified agents interact randomly and repeatedly choose alternatives from a circular space of color variants. Agents are endowed with a memory of past experiences and a boredom parameter, promoting avoidance of monotony. Simulating collective color trends with this model captures aspects of real trends observed in fashion magazines. We manipulate the two parameters and observe that the boredom parameter is essential for perpetuating fashion dynamics in our model. Furthermore, highly bored agents lead future population trends, when acting coherently or being highly popular. Taken together, our study illustrates that highly bored individuals can guide collective dynamics of a population to continuously explore different variants of behavior.

Distributed swarm system with hybrid-flocking control for small fixed-wing UAVs: Algorithms and flight experiments

This paper presents a distributed swarm system for small fixed-wing unmanned aerial vehicles (UAVs). In particular, to perform various missions with multiple UAVs that are densely gathered and collision free, a hybrid-flocking control algorithm is synthesized by using three types of control protocols: vector field guidance (for path following/loitering), augmented Cucker-Smale (ACS) model (for collective flocking behavior), and potential field (for collision avoidance). In particular, to address the issue of conflicts between different control protocols, the adaptive ACS model is proposed and the optimization problem is formulated to determine the suitable mixing weights of control protocols. We also design the transition of multiple operation modes and communication architecture for the swarm system. The system is evaluated using the proposed hybrid-flocking control algorithm by proof-of-concept real flight experiments using 18 small fixed-wing UAVs as well as extensive numerical simulations. Flight experiments are successfully performed for multiple consecutive tasks including the individual task, circular path loitering and elliptical path loitering while avoiding collisions among UAVs.

Individual differences of limitation to extract beat from Kuramoto coupled oscillators: Transition from beat-based tapping to frequent tapping with weaker coupling.

Musical performers synchronize to each other despite differences in sound-onset timings which reflect each musician's sense of the beat. A dynamical system of Kuramoto oscillators can simulate this spread of onsets at varying levels of temporal alignment with a variety of tempo and sound densities which also influence individual abilities for beat extraction. Here, we examined how people's sense of beat emerges when tapping with Kuramoto oscillators of varying coupling strengths which distribute onsets around periodic moments in time. We hypothesized that people tap regularly close to the sound onset density peaks when coupling is strong. When weaker coupling produces multiple inter-onset intervals that are more widely spread, people may interpret their variety and distributions differently in order to form a sense of beat. Experiment 1 with a small in-person cohort indeed showed a few individuals who responded with high frequency tapping to slightly weak coupled stimuli although the rest found regular beats. Experiment 2 with a larger on-line cohort revealed three groups based on characteristics of inter-tap-intervals analyzed by k-means clustering, namely a Regular group (about 1/3 of the final sample) with the most robust beat extraction, Fast group (1/6) who maintained frequent tapping except for the strongest coupling, and Hybrid group (1/2) who maintained beats except for the weakest coupling. Furthermore, the adaptation time course of tap interval variability was slowest in Regular group. We suggest that people's internal criterion for forming beats may involve different perceptual timescales where multiple stimulus intervals could be integrated or processed sequentially as is, and that the highly frequent tapping may reflect their approach in actively seeking synchronization. Our study provides the first documentation of the novel limits of sensorimotor synchronization and individual differences using coupled oscillator dynamics as a generative model of collective behavior.

Data-Driven Analysis and Modeling of Collective Generation Behaviors in an Electricity Market: A Perspective From Market Participants

Data-Driven Analysis and Modeling of Collective Generation Behaviors in an Electricity Market: A Perspective From Market Participants

A review on collective behavior modeling and simulation: building a link between cognitive psychology and physical action

A review on collective behavior modeling and simulation: building a link between cognitive psychology and physical action

The hybrid bio-robotic swarm as a powerful tool for collective motion research: a perspective.

Swarming or collective motion is ubiquitous in natural systems, and instrumental in many technological applications. Accordingly, research interest in this phenomenon is crossing discipline boundaries. A common major question is that of the intricate interactions between the individual, the group, and the environment. There are, however, major gaps in our understanding of swarming systems, very often due to the theoretical difficulty of relating embodied properties to the physical agents-individual animals or robots. Recently, there has been much progress in exploiting the complementary nature of the two disciplines: biology and robotics. This, unfortunately, is still uncommon in swarm research. Specifically, there are very few examples of joint research programs that investigate multiple biological and synthetic agents concomitantly. Here we present a novel research tool, enabling a unique, tightly integrated, bio-inspired, and robot-assisted study of major questions in swarm collective motion. Utilizing a quintessential model of collective behavior-locust nymphs and our recently developed Nymbots (locust-inspired robots)-we focus on fundamental questions and gaps in the scientific understanding of swarms, providing novel interdisciplinary insights and sharing ideas disciplines. The Nymbot-Locust bio-hybrid swarm enables the investigation of biology hypotheses that would be otherwise difficult, or even impossible to test, and to discover technological insights that might otherwise remain hidden from view.

Emergence of Adaptation of Collective Behavior Based on Visual Perception

Unmanned swarms are widespread used in the IoT. The ability of unmanned swarms to achieve adaptive collective behavior in complicated mission scenarios is a prerequisite for meeting mission objectives. However, classical collective behavior models often use the velocity and position of neighbors as inputs to be constructed from a phenomenological perspective. This complicates the construction of unmanned swarms and is incompatible with biological perception. Therefore, this paper proposes an Observation-Orientation-Decision-Action (OODA) framework for the construction of adaptive collective behavior based on visual perception, inspired by biological collective behavior formations. The model contains no explicit alignment, and no information exchange occurs between individuals. Instead, individuals make decisions based purely on the sight distance corresponding to different relative orientations. Based on adaptability evaluation metrics defined at the collective level, experiments including coordinated collective motion, single disturbed individual, single external disturbance, narrow passage, and multiple external disturbances scenarios show that the group can respond adaptively to different scenarios with a stable crystal structure while avoiding collisions. In addition to particle simulations, different scenarios provide validation using the Webots robot simulator. As a result, this approach compensates for the inadequacies of existing models and provides technical support for the application of unmanned swarms in various IoT scenarios.

Сходимость по норме динамики коллективного поведения в рефлексивной модели олигополии с лидерами

A model of oligopoly with an arbitrary number of rational agents that are reflexive according to Cournot or Stackelberg, under the conditions of incomplete information for the classical case of linear functions of costs and demand is considered. The problem of achieving equilibrium based on mathematical modeling agents' decision-making processes is investigated. Works in this direction are relevant due to the importance of understanding the processes in real markets and the convergence of theoretical models with them. In the framework of a dynamic model of reflexive collective behavior, each agent at each moment adjusts its output, making a step in the direction of output maximizing its profit under the expected choice of competitors. The permissible step value is set by the range. This article sets and solves the problem of finding the ranges of permissible steps of agents, which are formulated as conditions that guarantee the convergence of dynamics to equilibrium. The novelty of the study is determined by the use of the norm of the error transition matrix from the t-th to (t+1)-moment of time as a criterion of the dynamics convergence. It is shown that the dynamics converge if the norm is less than unity, starting at some point in time, and the failure to fulfill this criterion especially manifests itself in multidirectional choice, when some agents choose "big" steps towards their current goals, while others, on the contrary, choose "small" steps. Failure to meet the criterion also increases as the market grows. The general conditions for the ranges of convergence of dynamics for an arbitrary number of agents are established, and a method for constructing the maximum such ranges is proposed, which also constitutes the novelty of the study. The results of solving the above problems for particular cases of oligopoly, which are the most widespread in practice, are presented.

Approaches to Studying Collective Behavior Models in Competitive Markets: Peculiarities and Insights

The paper addresses the problem of achieving Nash equilibrium in an oligopoly market where common knowledge is absent. It explores two approaches to study the convergence conditions of the dynamics in a linear oligopoly model with any number of Cournot or Stackelberg reflexive agents.
 The first approach utilizes indicator functions to guide agents in adjusting their outputs to reach the optimum under existing competitors' outputs. The second approach uses norms of transition matrices from iteration to iteration in the computational process. The paper presents the authors' research results, including necessary mathematical lemmas and statements, and computational experiments with the models.
 The paper emphasizes several important features of the approaches, such as the conditions for individual agent choices that ensure the convergence to equilibrium of collective behavior dynamics for duopoly and any number of agents in the market, the convergence criteria of the dynamics, and the calculation of indicator functions and norms of transition matrices.

METHOD OF ROUTING A GROUP OF MOBILE ROBOTS IN A FIXED NETWORK FOR SEARCHING THE MISSING OBJECTS IN A TECHNOLOGICAL DISASTER ZONE

Context. The relevance of the article is determined by the need for further development of models of collective behavior of systems with multi-agent structure construction endowed with intelligence that ensures synchronization of the joint efforts of various agents while achieving the goals set for the system. The method proposed in the article solves the problem of competition between different agents of a multi-agent system, which is important while performing search, rescue, and monitoring tasks in crisis areas of various origins.
 Objective is to develop a method for determining the sufficient population of a multi-agent system and the optimal routes of movement of its individual elements in a stationary network for the most complete examination of a technological disaster zone (any given zone based on a certain transport network).
 Method. We implemented the concept of a dynamic programming to search for all possible edge-simple longest paths connecting the directed subsets of vertices-sources and vertices-sinks in the structure of the model weighted directed graph. To this end, the modified Dijkstra method was applied. The modification comprises representing the weights of the arcs of the modeling directed graph with the negative values, which are further used in calculations according to the Dijkstra method. After finding the next edgesimple longest path, the arcs that make up it are fixed in the memory of the computer system (in the route plan) and removed from the graph structure, and the process is iteratively repeated. The search for paths takes place as long as the transitive closure between the vertices that are part of the specified subsets of source vertices and sink vertices is preserved. The developed method makes it possible to find such a set of traffic routes for the elements of the multi-agent system, which maximizes the area examined by them in a technological disaster zone (or the number of checked objects on the traffic routes) in one “wave” of the search and distributes the elements of a multi-agent system by routes that do not have common areas. A derivative of the application of the developed method is the determination of a sufficient population of a multi-agent system for effective search activities within the defined zone.
 Results. 1) A method of routing a group of mobile robots in a stationary network for searching the missing objects in a technological disaster zone has been developed. 2) The working expression of the Dijkstra method for searching in the structure of a network object (in the structure of a model graph) for the longest paths has been formalized. 3) We have suggested a set of indicators for a comprehensive evaluation of route plans of a multi-agent system. 4) The method has been verified on test problems.
 Conclusions. Theoretical studies and several experiments confirm the efficiency of the developed method. The solutions made using the developed method are accurate, which allows recommending it for practical use in determining in an automated mode route plans for multi-agent systems, as well as the required number of agents in such systems to perform the required amount of search tasks in a particular crisis area.

Equilibria and energy minimizers for an interaction model on the hyperbolic space

We study an intrinsic model for collective behaviour on the hyperbolic space Hn. We investigate the equilibria of the aggregation equation (or equivalently, the critical points of the associated interaction energy) for interaction potentials that include Newtonian repulsion. By using the method of moving planes, we establish the radial symmetry and the monotonicity of equilibria supported on geodesic balls of Hn. We find several explicit forms of equilibria and show that one such equilibrium is a global energy minimizer. We also consider more general potentials and utilize a technique used for Rn to establish the existence of compactly supported global minimizers. Numerical simulations are presented, suggesting that some of the equilibria studied here are global attractors. The key tool in our investigations is a family of isometries of Hn that we have developed for this purpose.

Non-mean-field Vicsek-type models for collective behavior

We consider interacting particle dynamics with Vicsek-type interactions, and their macroscopic Partial Differential Equation (PDE) limit, in the non-mean-field regime; that is, we consider the case in which each particle/agent in the system interacts only with a prescribed subset of the particles in the system (for example, those within a certain distance). In this non-mean-field regime the influence between agents (i.e. the interaction term) can be normalized either by the total number of agents in the system (global scaling) or by the number of agents with which the particle is effectively interacting (local scaling). We compare the behavior of the globally scaled and the locally scaled systems in many respects, considering for each scaling both the PDE and the corresponding particle model. In particular, we observe that both the locally and globally scaled particle system exhibit pattern formation (i.e. formation of traveling-wave-like solutions) within certain parameter regimes, and generally display similar dynamics. The same is not true of the corresponding PDE models. Indeed, while both PDE models have multiple stationary states, for the globally scaled PDE such (space-homogeneous) equilibria are unstable for certain parameter regimes, with the instability leading to traveling wave solutions, while they are always stable for the locally scaled one, which never produces traveling waves. This observation is based on a careful numerical study of the model, supported by further analysis.

OptiSwarm: Optical Swarm Robots Using Implicit Cooperation

Swarm robots have always served as verification platforms and deployment tools for swarming models that usually take relative distances, bearing angles, velocity directions, or differentiation of neighbors as inputs to regulate individual motion. With natural decentralization and high scalability, existing swarm robotic platforms based on purely implicit cooperation exhibit excellent potential for evaluating and deploying swarming models in denied environments. However, most of the current implicit cooperation platforms are limited in their adaptability because they are hardly capable of providing the above four inputs without external assistance. To address this problem, this article presents optiSwarm, a swarm robotic platform, where each robot (Cubot) within this platform is based on a novel implicit cooperation system. Cubot can not only directly obtain relative distances, bearing angles, and differentiation of adjacent robots through vision-based local rules but also has a relative velocity direction perception mechanism purely on implicit communication. The robot’s perception is proven to be reliable through real-world tests. Through implementing three collective behaviors guided by diverse inputs, optiSwarm is employed and evaluated in typical scenarios demonstrating that it is capable of verifying models of collective behaviors.

Automated optimization of multilevel models of collective behaviour: application to mixed society of animals and robots

Animal societies exhibit complex dynamics that require multi-level descriptions. They are difficult to model, as they encompass information at different levels of description, such as individual physiology, individual behaviour, group behaviour and features of the environment. The collective behaviour of a group of animals can be modelled as a dynamical system. Typically, models of behaviour are either macroscopic (differential equations of population dynamics) or microscopic (such as Markov chains, explicitly specifying the spatio-temporal state of each individual). These two kind of models offer distinct and complementary descriptions of the observed behaviour. Macroscopic models offer mean field description of the collective dynamics, where collective choices are considered as the stable steady states of a nonlinear system governed by control parameters leading to bifurcation diagrams. Microscopic models can be used to perform computer simulations or as building blocks for robot controllers, at the individual level, of the observed spatial behaviour of animals. Here, we present a methodology to translate a macroscopic model into different microscopic models. We automatically calibrate the microscopic models so that the resulting simulated collective dynamics fit the solutions of the reference macroscopic model for a set of parameter values corresponding to a bifurcation diagram leading to multiple steady states. We apply evolutionary algorithms to simultaneously optimize the parameters of the models at different levels of description. This methodology is applied, in simulation, to an experimentally validated shelter-selection problem solved by gregarious insects and robots. Our framework can be used for multi-level modelling of collective behaviour in animals and robots.

The role of effective communication in the process of forming a cohesive and motivated team

In today's globalized world, the success of any activity depends not only on the professionalism and personal qualities of individual employees, but also on the effectively established relationships of the whole team. The manager's ability to communicate with subordinates and properly build productive relationships with them, the desire of team members to hear each other and take care of successful tasks, ensure coordinated work, where each team member is ready to direct their skills and knowledge to solve common problems. A strong, unified team is the basis for the effective operation of both individual structural elements and the organization as a whole. That is why the problem of effectively established team communication as a key condition for creating a cohesive and motivated team is extremely relevant. Analysis of recent sources of research and publications. Many foreign scholars have devoted their research to the problem of teamwork. In particular, the general problems of teamwork are devoted to the work of J.R. Kemsenber, K. Lewis-McClear, D.K. Smith, M. Taylor. The main directions of development of small groups were studied by B. Tuckman. M. Belbin's works are devoted to the study of the main roles played by team members in the process of their work. V. Voropaiev, Y. Yakutin, L. Kalinichenko, V. Zanora and many other scientists devoted their research to the problem of team management in the context of project implementation. Most of the current work on the study of command systems and models of collective behavior addresses the general problems of team management, but insufficiently addresses issues related to establishing effective communication to form a cohesive and motivated team. The subject of research is the role of communication in team building as an effective tool for forming a professional team. The purpose of writing this article is to identify the features, methods and tools of team communication that are used to convey messages about the coordination of interaction, labor and intellectual efforts of the team and contribute to the cohesion and motivation of team members. The results of the work can find their practical application in the management of modern domestic enterprises and organizations.

From Modelling Turbulence to General Systems Modelling

Complex adaptive and evolutionary systems can, at least in principle, be modelled in ways that are similar to modelling of complex mechanical (or physical) systems. While quantitative modelling of turbulent reacting flows has been developed over many decades due to availability of experimental data, modelling of complex evolutionary systems is still in its infancy and has huge potential for further development. This work analyses recent trends, points to the similarity of modelling approaches used in seemingly different areas, and suggests a basic classification for such approaches. Availability of data in the modern computerised world allows us to use tools previously developed in physics and applied mathematics in new domains of scientific inquiry that previously were not amendable by quantitative evaluation and modelling, while raising concerns about the associated ethical and legal issues. While the utility of big data has been repeatedly demonstrated in various practical applications, these applications, as far as we can judge, do not involve the scientific goal of conceptual modelling of emergent collective behaviour in complex evolutionary systems.

Modeling the Dynamics of Collective Behavior in a Reflexive Game with an Arbitrary Number of Leaders

An oligopoly with an arbitrary number of Stackelberg leaders under incomplete, asymmetrical agents' awareness and inadequacy of their predictions of competitors' actions is considered. Models of individual decision-making processes by agents are studied. The reflexive games theory and collective behavior theory are the theoretical basis for construction and analytical study process models. They complement each other in that reflexive games allow using the collective behavior procedures and the results of agents' reflections, leading to a Nash equilibrium. The dynamic decision-making process considered repeated static games on a range of agents' feasible responses to the expected actions of the environment, considering current economic restrictions and competitiveness in each game. Each reflexive agent in each game calculates its current goal position and changes its state, taking steps towards the current position of the goal to obtain positive profit or minimize losses. Sufficient conditions for the convergence of processes in discrete time for the case of linear costs of agents and linear demand is the main result of this work. New analytical expressions for the agents' current steps' ranges guarantee the convergence of the collective behavior models to static Nash equilibrium is obtained. That allows each agent to maximize their profit, assuming common knowledge among the agents. The processes when the agent chooses their best response are also analyzed. The latter may not give converging trajectories. The case of the duopoly in comparison with modern results is discussed in detail. Necessary mathematical lemmas, statements, and their proofs are presented.

Comprehensive evaluation of the intelligence levels for unmanned swarms based on the collective OODA loop and group extension cloud model

Considering the increasing complexity of application scenarios, the evaluation of the intelligence levels for unmanned swarms has attracted scholarly attention. However, the existing evaluation studies cannot suitably reflect the intelligence of unmanned swarms, and they rarely provide a specific evaluation process. By introducing the collective intelligent behavior model for unmanned swarms based on the collective Observe–Orient–Decide–Act (OODA) loop, this study constructs a comprehensive evaluation index system that can systematically reflect the overall intelligence of unmanned swarms in complex scenarios. Considering the fuzziness and randomness in the processes of weight calculation and level evaluation, this study proposes a comprehensive evaluation method of the intelligence levels for unmanned swarms based on a group extension cloud model. This method calculates the weights of various evaluation indexes at different layers by adopting the group extension analytic hierarchy process. Moreover, it obtains the comprehensive evaluation conclusion of the intelligence levels for unmanned swarms by adopting the cloud model. Applying the proposed method, this study evaluates two specific types of unmanned aerial vehicle swarms. The results show that the proposed method can more flexibly and accurately evaluate the intelligence levels of unmanned swarms than the previous fully qualitative methods.

Modeling of Collective Evacuation Behavior with Conformity Bias and Passivity-based Nudging Design

Modeling of Collective Evacuation Behavior with Conformity Bias and Passivity-based Nudging Design