IEEE Transactions on Automatic Control, ISSN 0018-9286, 11/2017, Volume 62, Issue 11, pp. 5866 - 5872

This technical note studies the well-known Vicsek model with bounded time-varying delays. We consider the case that the communication delays appear in both...

multi-agent systems | Simulation | Delay effects | Robustness | Delays | Delayed Vicsek models | Synchronization | Mathematical model | Physics | synchronization | MULTIAGENT SYSTEMS | CONSENSUS | COORDINATION | AGENTS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Delay lines | Usage | Mathematical models | Research

multi-agent systems | Simulation | Delay effects | Robustness | Delays | Delayed Vicsek models | Synchronization | Mathematical model | Physics | synchronization | MULTIAGENT SYSTEMS | CONSENSUS | COORDINATION | AGENTS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Delay lines | Usage | Mathematical models | Research

Journal Article

Multiscale Modeling and Simulation, ISSN 1540-3459, 2016, Volume 14, Issue 3, pp. 1063 - 1088

We consider a collective behavior model in which individuals try to imitate each others' velocity and have a preferred speed. We show that a phase change...

Vicsek model | Flocking model | Cucker-Smale model | Phase transition | DRIVEN PARTICLES | SYSTEM | SELF-STABILIZING PROCESSES | flocking model | EQUATIONS | PHYSICS, MATHEMATICAL | ORDER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DYNAMICS | FISH | CONVERGENCE | phase transition | MEAN-FIELD LIMIT | MULTI-WELLS LANDSCAPE | Dynamical Systems | Mathematics

Vicsek model | Flocking model | Cucker-Smale model | Phase transition | DRIVEN PARTICLES | SYSTEM | SELF-STABILIZING PROCESSES | flocking model | EQUATIONS | PHYSICS, MATHEMATICAL | ORDER | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DYNAMICS | FISH | CONVERGENCE | phase transition | MEAN-FIELD LIMIT | MULTI-WELLS LANDSCAPE | Dynamical Systems | Mathematics

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 09/2015, Volume 297, Issue C, pp. 32 - 46

In this paper we present the first numerical method for a kinetic description of the Vicsek swarming model. The kinetic model poses a unique challenge, as...

Finite Volume method | Spectral method | Vicsek model | Hyperbolic systems | Kinetic equation | SYSTEM | BEHAVIOR | LIMIT | SCHOOLS | COLLISION OPERATOR | PHYSICS, MATHEMATICAL | SELF-DRIVEN PARTICLES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | BOLTZMANN-EQUATION | CONTINUUM MODEL | FLOCKING | Computation | Mathematical models | Spectra | Representations | Swarming | Invariants | Spectral methods | Optimization | MATHEMATICS AND COMPUTING

Finite Volume method | Spectral method | Vicsek model | Hyperbolic systems | Kinetic equation | SYSTEM | BEHAVIOR | LIMIT | SCHOOLS | COLLISION OPERATOR | PHYSICS, MATHEMATICAL | SELF-DRIVEN PARTICLES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | BOLTZMANN-EQUATION | CONTINUUM MODEL | FLOCKING | Computation | Mathematical models | Spectra | Representations | Swarming | Invariants | Spectral methods | Optimization | MATHEMATICS AND COMPUTING

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 07/2018, Volume 502, pp. 590 - 604

We study the temporal correlations in the evolution of the order parameter ϕt for the Vicsek model with vectorial noise by estimating its Hurst exponent H with...

Fractality | Scaling range | Detrended Fluctuation Analysis | Vicsek model | Time series analysis | Self-propelled particles | PHYSICS, MULTIDISCIPLINARY | FLOCKS | TERM-MEMORY | SCALING RANGES | MULTIFRACTALITY | PHASE-TRANSITION | ISING-MODEL | TIME-SERIES | LONG-RANGE CORRELATIONS

Fractality | Scaling range | Detrended Fluctuation Analysis | Vicsek model | Time series analysis | Self-propelled particles | PHYSICS, MULTIDISCIPLINARY | FLOCKS | TERM-MEMORY | SCALING RANGES | MULTIFRACTALITY | PHASE-TRANSITION | ISING-MODEL | TIME-SERIES | LONG-RANGE CORRELATIONS

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 02/2017, Volume 62, Issue 2, pp. 636 - 651

Natural systems are inextricably affected by noise. Within recent decades, the manner in which noise affects the collective behavior of self-organized systems,...

Analytical models | Vicsek model | Biological system modeling | heterogeneous multi-agent system | Sociology | Boundary conditions | Robustness | Mathematical model | robust consensus | self-propelled particles | Statistics | Collective motion | STATISTICAL-MECHANICS | MULTIAGENT SYSTEMS | HYDRODYNAMICS | ALGORITHMS | ENGINEERING, ELECTRICAL & ELECTRONIC | ORDER | PHASE-TRANSITION | DYNAMICS | CONVERGENCE | AUTOMATION & CONTROL SYSTEMS | FLOCKING | Usage | Mathematical models | Research | Nonlinear dynamics | Complex systems | Mathematics - Optimization and Control

Analytical models | Vicsek model | Biological system modeling | heterogeneous multi-agent system | Sociology | Boundary conditions | Robustness | Mathematical model | robust consensus | self-propelled particles | Statistics | Collective motion | STATISTICAL-MECHANICS | MULTIAGENT SYSTEMS | HYDRODYNAMICS | ALGORITHMS | ENGINEERING, ELECTRICAL & ELECTRONIC | ORDER | PHASE-TRANSITION | DYNAMICS | CONVERGENCE | AUTOMATION & CONTROL SYSTEMS | FLOCKING | Usage | Mathematical models | Research | Nonlinear dynamics | Complex systems | Mathematics - Optimization and Control

Journal Article

Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 06/2017, Volume 27, Issue 6, pp. 1005 - 1049

We present a new model for multi-agent dynamics where each agent is described by its position and body attitude: agents travel at a constant speed in a given...

generalized collision invariant | rotation group | Vicsek model | collective motion | Body attitude coordination | DRIVEN PARTICLES | SELF-PROPELLED PARTICLES | MATHEMATICS, APPLIED | HYDRODYNAMICS | LIMIT | CORPORA | SUPPLY CHAINS | ROTATIONS | PHASE-TRANSITION | DYNAMICS

generalized collision invariant | rotation group | Vicsek model | collective motion | Body attitude coordination | DRIVEN PARTICLES | SELF-PROPELLED PARTICLES | MATHEMATICS, APPLIED | HYDRODYNAMICS | LIMIT | CORPORA | SUPPLY CHAINS | ROTATIONS | PHASE-TRANSITION | DYNAMICS

Journal Article

Journal of Physics D: Applied Physics, ISSN 0022-3727, 03/2018, Volume 51, Issue 13, p. 134004

Collective motion is of interest to laymen and scientists in different fields. In groups of animals, many patterns of collective motion arise such as polarized...

Vicsek model | collective behaviour | self-propelled particles | milling | SYSTEM | COLLECTIVE MOTION | SHAPE | PHYSICS, APPLIED

Vicsek model | collective behaviour | self-propelled particles | milling | SYSTEM | COLLECTIVE MOTION | SHAPE | PHYSICS, APPLIED

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 2012, Volume 25, Issue 3, pp. 339 - 343

We consider the continuous version of the Vicsek model with noise, proposed as a model for collective behaviour of individuals with a fixed speed. We...

Vicsek model | Collective behaviour | Mean-field limit | Interacting particle systems | MATHEMATICS, APPLIED | SELF-DRIVEN PARTICLES | Analysis | Models | Differential equations | Law | Infinity | Partial differential equations | Noise | Uniqueness | Joining | Mathematical models | Convergence | Probability | Analysis of PDEs | Mathematics

Vicsek model | Collective behaviour | Mean-field limit | Interacting particle systems | MATHEMATICS, APPLIED | SELF-DRIVEN PARTICLES | Analysis | Models | Differential equations | Law | Infinity | Partial differential equations | Noise | Uniqueness | Joining | Mathematical models | Convergence | Probability | Analysis of PDEs | Mathematics

Journal Article

9.
Full Text
Tricritical points in a Vicsek model of self-propelled particles with bounded confidence

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 12/2014, Volume 90, Issue 6, p. 063315

We study the orientational ordering in systems of self-propelled particles with selective interactions. To introduce the selectivity we augment the standard...

COLLECTIVE MOTION | PHYSICS, FLUIDS & PLASMAS | PHASE-TRANSITIONS | BEHAVIOR | SMALL SYSTEMS | DYNAMICS | HYDRODYNAMICS | MOVEMENT | GINZBURG-LANDAU APPROACH | PHYSICS, MATHEMATICAL | ACTIVE MATTER | Models, Theoretical | Motion | Kinetics | bounded confidence | nematic transition | Annan fysik | Mathematics | self-propelled particles | Physics | Fysik | Physical Sciences | Vicsek model | Naturvetenskap | Other Physics Topics | Natural Sciences | Matematik

COLLECTIVE MOTION | PHYSICS, FLUIDS & PLASMAS | PHASE-TRANSITIONS | BEHAVIOR | SMALL SYSTEMS | DYNAMICS | HYDRODYNAMICS | MOVEMENT | GINZBURG-LANDAU APPROACH | PHYSICS, MATHEMATICAL | ACTIVE MATTER | Models, Theoretical | Motion | Kinetics | bounded confidence | nematic transition | Annan fysik | Mathematics | self-propelled particles | Physics | Fysik | Physical Sciences | Vicsek model | Naturvetenskap | Other Physics Topics | Natural Sciences | Matematik

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 2010, Volume 389, Issue 21, pp. 4552 - 4557

The growth of the modified Family model and the Etching model on the Sierpinski carpet is studied by means of numerical simulations. The evolving interface of...

Family–Vicsek dynamic scaling | Sierpinski carpet | FamilyVicsek dynamic scaling | EXPONENTS | Family-Vicsek dynamic scaling | PHYSICS, MULTIDISCIPLINARY | Aggregates | Mathematical analysis | Fractal analysis | Etching | Mathematical models | Deviation | Statistical mechanics | Deposition

Family–Vicsek dynamic scaling | Sierpinski carpet | FamilyVicsek dynamic scaling | EXPONENTS | Family-Vicsek dynamic scaling | PHYSICS, MULTIDISCIPLINARY | Aggregates | Mathematical analysis | Fractal analysis | Etching | Mathematical models | Deviation | Statistical mechanics | Deposition

Journal Article

11.
Full Text
Flocking Dynamics of the Inertial Spin Model with a Multiplicative Communication Weight

Journal of Nonlinear Science, ISSN 0938-8974, 8/2019, Volume 29, Issue 4, pp. 1301 - 1342

In this paper, we study a flocking dynamics of the deterministic inertial spin (IS) model. The IS model was introduced for the collective dynamics of active...

The Vicsek model | 34C15 | Cucker–Smale model | 82C22 | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | Mathematics | Inertial spin model | 34D05 | Flocking | Analysis | Mathematical and Computational Engineering | Unit speed constraint | EMERGENT BEHAVIOR | SYSTEM | MATHEMATICS, APPLIED | CONTINUUM-LIMIT | PHYSICS, MATHEMATICAL | SELF-DRIVEN PARTICLES | COLLECTIVE MOTION | MECHANICS | Cucker-Smale model | Models | Numerical analysis

The Vicsek model | 34C15 | Cucker–Smale model | 82C22 | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | Mathematics | Inertial spin model | 34D05 | Flocking | Analysis | Mathematical and Computational Engineering | Unit speed constraint | EMERGENT BEHAVIOR | SYSTEM | MATHEMATICS, APPLIED | CONTINUUM-LIMIT | PHYSICS, MATHEMATICAL | SELF-DRIVEN PARTICLES | COLLECTIVE MOTION | MECHANICS | Cucker-Smale model | Models | Numerical analysis

Journal Article

Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 07/2012, Volume 22, Issue 7

We consider the macroscopic model derived by Degond and Motsch from a time-continuous version of the Vicsek model, describing the interaction orientation in a...

asymptotic study | orientation interaction | Vicsek model | collisional invariants | non-hyperbolicity | anisotropy | DRIVEN PARTICLES | SYSTEM | MATHEMATICS, APPLIED | TRAFFIC FLOW | SIMULATION | MOTION | PERSISTENT TURNING WALKER | FISH | MOVEMENT | DIFFUSION | FLOCKING

asymptotic study | orientation interaction | Vicsek model | collisional invariants | non-hyperbolicity | anisotropy | DRIVEN PARTICLES | SYSTEM | MATHEMATICS, APPLIED | TRAFFIC FLOW | SIMULATION | MOTION | PERSISTENT TURNING WALKER | FISH | MOVEMENT | DIFFUSION | FLOCKING

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 08/2013, Volume 392, Issue 16, pp. 3329 - 3334

In this paper, we study a weighted self-propelled agent system, wherein each agent’s direction is affected by its spatial neighbors with different impacts. In...

Self-propelled agent system | Collective dynamics | Vicsek model | PHYSICS, MULTIDISCIPLINARY | ORDER | Multiagent systems | Computer simulation | Mathematical models | Biological | Statistical mechanics | Optimization | Convergence

Self-propelled agent system | Collective dynamics | Vicsek model | PHYSICS, MULTIDISCIPLINARY | ORDER | Multiagent systems | Computer simulation | Mathematical models | Biological | Statistical mechanics | Optimization | Convergence

Journal Article

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2017, Volume 10413, pp. 89 - 102

Conference Proceeding

Journal of Statistical Physics, ISSN 0022-4715, 10/2013, Volume 153, Issue 2, pp. 270 - 288

In flocking models, the collective motion of self-driven individuals leads to the formation of complex spatiotemporal patterns. The Standard Vicsek Model (SVM)...

Vicsek model | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Complex networks | Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Physics | Self-propelled particle systems | Collective motion | ORDER | PHASE-TRANSITIONS | DYNAMICS | ABSENCE | PHYSICS, MATHEMATICAL

Vicsek model | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Complex networks | Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Physics | Self-propelled particle systems | Collective motion | ORDER | PHASE-TRANSITIONS | DYNAMICS | ABSENCE | PHYSICS, MATHEMATICAL

Journal Article

Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 06/2017, Volume 27, Issue 7, pp. 1255 - 1299

The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic...

Vicsek model | generalized collision invariants | swarming | Vlasov-like equations | Cucker-Smale model | Laplace-Beltrami operator | measure solutions | DRIVEN PARTICLES | MATHEMATICS, APPLIED | MAGNETIC-FIELDS | CONTINUUM-LIMIT | LARMOR RADIUS APPROXIMATION | ASYMPTOTIC FLOCKING | PHASE-TRANSITION | BOLTZMANN-EQUATION | PLANCK-LANDAU EQUATION | ANIMAL GROUPS | MEAN-FIELD LIMIT

Vicsek model | generalized collision invariants | swarming | Vlasov-like equations | Cucker-Smale model | Laplace-Beltrami operator | measure solutions | DRIVEN PARTICLES | MATHEMATICS, APPLIED | MAGNETIC-FIELDS | CONTINUUM-LIMIT | LARMOR RADIUS APPROXIMATION | ASYMPTOTIC FLOCKING | PHASE-TRANSITION | BOLTZMANN-EQUATION | PLANCK-LANDAU EQUATION | ANIMAL GROUPS | MEAN-FIELD LIMIT

Journal Article

MATHEMATICAL BIOSCIENCES AND ENGINEERING, ISSN 1547-1063, 2019, Volume 16, Issue 6, pp. 7883 - 7910

We analyse the asymptotic behavior for kinetic models describing the collective behavior of animal populations. We focus on models for self-propelled...

EMERGENT BEHAVIOR | SYSTEM | PARTICLE | swarming | CONTINUUM-LIMIT | EQUATIONS | ASYMPTOTIC FLOCKING | Vicsek model | COLLECTIVE MOTION | PHASE-TRANSITION | MATHEMATICAL & COMPUTATIONAL BIOLOGY | Vlasov-like equations | FLUID DYNAMIC LIMITS | Cucker-Smale model | MEAN-FIELD LIMIT | Mathematics

EMERGENT BEHAVIOR | SYSTEM | PARTICLE | swarming | CONTINUUM-LIMIT | EQUATIONS | ASYMPTOTIC FLOCKING | Vicsek model | COLLECTIVE MOTION | PHASE-TRANSITION | MATHEMATICAL & COMPUTATIONAL BIOLOGY | Vlasov-like equations | FLUID DYNAMIC LIMITS | Cucker-Smale model | MEAN-FIELD LIMIT | Mathematics

Journal Article

KINETIC AND RELATED MODELS, ISSN 1937-5093, 08/2019, Volume 12, Issue 4, pp. 791 - 827

We introduce and analyse a continuum model for an interacting particle system of Vicsek type. The model is given by a non-linear kinetic partial differential...

EXISTENCE | SYSTEM | HYDRODYNAMIC LIMIT | MATHEMATICS, APPLIED | self-organization | scaling limit of interacting particle systems | EQUATIONS | PATTERNS | COLLECTIVE BEHAVIOR | non ergodic McKean-Vlasov process | MATHEMATICS | ORDER | Vicsek model | PHASE-TRANSITION | DYNAMICS | Nonlinear kinetic PDEs

EXISTENCE | SYSTEM | HYDRODYNAMIC LIMIT | MATHEMATICS, APPLIED | self-organization | scaling limit of interacting particle systems | EQUATIONS | PATTERNS | COLLECTIVE BEHAVIOR | non ergodic McKean-Vlasov process | MATHEMATICS | ORDER | Vicsek model | PHASE-TRANSITION | DYNAMICS | Nonlinear kinetic PDEs

Journal Article

Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 12/2015, Volume 25, Issue 13, pp. 2439 - 2475

We present an individual-based model describing disk-like self-propelled particles moving inside parallel planes. The disk directions of motion follow...

generalized collision invariant | Vicsek model | Fokker-Planck equation | Self-organized hydrodynamics | DRIVEN PARTICLES | SYSTEM | MATHEMATICS, APPLIED | FLOCKS | CONTINUUM-LIMIT | HYDRODYNAMICS | CONSTRAINTS | COLLECTIVE BEHAVIOR

generalized collision invariant | Vicsek model | Fokker-Planck equation | Self-organized hydrodynamics | DRIVEN PARTICLES | SYSTEM | MATHEMATICS, APPLIED | FLOCKS | CONTINUUM-LIMIT | HYDRODYNAMICS | CONSTRAINTS | COLLECTIVE BEHAVIOR

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 05/2013, Volume 392, Issue 10, pp. 2398 - 2405

Large flocks of wild beings can have coordinated motion with neither leading center nor global information. The Vicsek model and its new versions explained...

Vicsek model | Restricted visual field | Convergence time | Exponential neighbor weight | Direction consensus | PHYSICS, MULTIDISCIPLINARY | FLOCKS | CONSENSUS | COORDINATION | NETWORKS | PREDICTIVE MECHANISMS | TRANSITION | COLLECTIVE MOTION | ANIMAL GROUPS | COMMUNICATION

Vicsek model | Restricted visual field | Convergence time | Exponential neighbor weight | Direction consensus | PHYSICS, MULTIDISCIPLINARY | FLOCKS | CONSENSUS | COORDINATION | NETWORKS | PREDICTIVE MECHANISMS | TRANSITION | COLLECTIVE MOTION | ANIMAL GROUPS | COMMUNICATION

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.