Inherent noise can facilitate coherence in collective swarm motion
Open accessAbstract
Among the most striking aspects of the movement of many animal groups are their sudden coherent changes in direction. Recent observations of locusts and starlings have shown that this directional switching is an intrinsic property of their motion. Similar direction switches are seen in self-propelled particle and other models of group motion. Comprehending the factors that determine such switches is key to understanding the movement of these groups. Here, we adopt a coarse-grained approach to the study of directional switching in a self-propelled particle model assuming an underlying one-dimensional Fokker–Planck equation for the mean velocity of the particles. We continue with this assumption in analyzing experimental data on locusts and use a similar systematic Fokker–Planck equation coefficient estimation approach to extract the relevant information for the assumed Fokker–Planck equation underlying that experimental data. In the experiment itself the motion of groups of 5 to 100 locust nymphs was investigated in a homogeneous laboratory environment, helping us to establish the intrinsic dynamics of locust marching bands. We determine the mean time between direction switches as a function of group density for the experimental data and the self-propelled particle model. This systematic approach allows us to identify key differences between the experimental data and the model, revealing that individual locusts appear to increase the randomness of their movements in response to a loss of alignment by the group. We give a quantitative description of how locusts use noise to maintain swarm alignment. We discuss further how properties of individual animal behavior, inferred by using the Fokker–Planck equation coefficient estimation approach, can be implemented in the self-propelled particle model to replicate qualitatively the group level dynamics seen in the experimental data.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Noise can facilitate coherence.
“facilitate coherence”
From Stewardship of global collective behavior (2021) · cites this paper as [101]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Novel Type of Phase Transition in a System of Self-Driven Particles
Vicsek, T., Czirók, A., Ben‐Jacob, E., Cohen, I., & Shochet, O. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.1226 · Cited by 7,395 · see citing works
Traffic and related self-driven many-particle systems
Helbing, D. (2001) · Reviews of Modern Physics · doi:10.1103/revmodphys.73.1067 · Cited by 3,226 · see citing works
Ballerini, M., Cabibbo, N., Candelier, R., Cavagna, A., Cisbani, E., Giardina, I., Lecomte, V., Orlandi, A., Giorgio Parisi, A., Procaccini, A., et al. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0711437105 · Cited by 1,978 · see citing works
Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance
Douglass, J. K., Wilkens, L. A., Pantazelou, E., & Moss, F. (1993) · Nature · doi:10.1038/365337a0 · Cited by 1,433 · see citing works
Complexity, Pattern, and Evolutionary Trade-Offs in Animal Aggregation
Parrish, J. K., & Leah Edelstein-keshet, A. (1999) · Science · doi:10.1126/science.284.5411.99 · Cited by 1,230 · see citing works
From Disorder to Order in Marching Locusts
Buhl, C., Sumpter, D. J. T., Couzin, I. D., Hale, J. J., Despland, E., Miller, E. R., & Simpson, S. J. (2006) · Science · doi:10.1126/science.1125142 · Cited by 1,153 · see citing works
Self-citationThe principles of collective animal behaviour
Sumpter, D. J. T. (2005) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2005.1733 · Cited by 1,019 · see citing works
Self-citationSelf-Organization and Collective Behavior in Vertebrates
Couzin, I. D., & Krause, J. (2003) · Advances in the study of behavior · doi:10.1016/s0065-3454(03)01001-5 · Cited by 921 · see citing works
Self-citationGear, C. W., Hyman, J. M., Kevrekidid, P. G., Kevrekidis, I. G., Runborg, O., & Theodoropoulos, C. (2003) · Communications in Mathematical Sciences · doi:10.4310/cms.2003.v1.n4.a5 · Cited by 778 · see citing works
Self-citationSelf-Organized Fish Schools: An Examination of Emergent Properties
Parrish, J. K., Viscido, S. V., & Grünbaum, D. (2002) · Biological Bulletin · doi:10.2307/1543482 · Cited by 706 · see citing works
The Structure and Function of Fish Schools
Partridge, B. L. (1982) · Scientific American · doi:10.1038/scientificamerican0682-114 · Cited by 643 · see citing works
Markov processes — an introduction for physical scientists
(1992) · Mathematics and Computers in Simulation · doi:10.1016/0378-4754(92)90114-v · Cited by 562 · see citing works
Collective Motion and Cannibalism in Locust Migratory Bands
Bazazi, S., Buhl, C., Hale, J. J., Anstey, M. L., Sword, G. A., Simpson, S. J., & Couzin, I. D. (2008) · Current Biology · doi:10.1016/j.cub.2008.04.035 · Cited by 328 · see citing works
Self-citationSingle-electron tunneling spectroscopy of single C_ in double-barrier tunnel junction
Lin, B.-F. (2006) · The Journal of Chemical Physics · Cited by 322 · see citing works
Schooling in the ecology of fish
Radakov, D. V. (1973) · Medical Entomology and Zoology · Cited by 289 · see citing works
From Compromise to Leadership in Pigeon Homing
Biro, D., Sumpter, D. J. T., Meade, J., & Guilford, T. (2006) · Current Biology · doi:10.1016/j.cub.2006.08.087 · Cited by 287 · see citing works
Self-citationCollective Motion of Self-Propelled Particles: Kinetic Phase Transition in One Dimension
Czirók, A., Barabási, A.-Ĺ., & Vicsek, T. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.209 · Cited by 275 · see citing works
The three-dimensional structure of fish schools
Partridge, B. L., Pitcher, T. J., Cullen, J. M., & Wilson, J. (1980) · Behavioral Ecology and Sociobiology · doi:10.1007/bf00292770 · Cited by 240 · see citing works
A Boltzmann-Like Approach for Traffic Flow
Prigogine, I., & Andrews, F. C. (1960) · Operations Research · doi:10.1287/opre.8.6.789 · Cited by 220 · see citing works
Information transfer in moving animal groups
Sumpter, D. J. T., Buhl, C., Biro, D., & Couzin, I. D. (2008) · Theory in Biosciences · doi:10.1007/s12064-008-0040-1 · Cited by 159 · see citing works
Self-citationModelling spatial dynamics of fish
Giske, J., Huse, G., & Fiksen, Ø. (1998) · Reviews in Fish Biology and Fisheries · doi:10.1023/a:1008864517488 · Cited by 134 · see citing works
Fluctuations and Scaling in Biology
(2001) · doi:10.1093/oso/9780198507895.001.0001 · Cited by 123 · see citing works
Gene regulatory networks: A coarse-grained, equation-free approach to multiscale computationPreprint
Erban, R., Kevrekidis, I. G., Elston, T. C., & Elston, T. C. (2005) · Cited by 83 · see citing works
Self-citationModels for tuna school formation
Stöcker, S. (1999) · Mathematical Biosciences · doi:10.1016/s0025-5564(98)10065-2 · Cited by 81 · see citing works
Gene regulatory networks: A coarse-grained, equation-free approach to multiscale computation
Erban, R., Kevrekidis, I. G., Adalsteinsson, D., & Elston, T. C. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2149854 · Cited by 71 · see citing works
Self-citationMathematical Modeling of Traffic Flows
Швецов, В. (2003) · Automation and Remote Control · doi:10.1023/a:1027348026919 · Cited by 60 · see citing works
Apparent Hysteresis in a Driven System with Self-Organized Drag
Haataja, M., Srolovitz, D. J., & Kevrekidis, I. G. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.160603 · Cited by 30 · see citing works
Self-citation
Flagged first, then by citations
Research works printed but not linked: 1
- [6]Partridge BL. The 3D structure of fish schools. Behav Ecol Sociobiol. 1980;6(4):277–288. [Google Scholar]
Cited by
Sorted by citations
Vicsek, T., & Zafeiris, A. (2012) · Physics Reports · doi:10.1016/j.physrep.2012.03.004 · Cited by 2,923 · see citing works
Romańczuk, P., Bär, M., Ebeling, W., Lindner, B., & Schimansky-Geier, L. (2012) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2012-01529-y · Cited by 1,115 · see citing works
Scale-free correlations in starling flocks
Cavagna, A., Cimarelli, A., Giardina, I., Giorgio Parisi, A., Santagati, R., Stefanini, F., & Viale, M. (2010) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1005766107 · Cited by 1,069 · see citing works
Collective States, Multistability and Transitional Behavior in Schooling Fish
Tunstrøm, K., Katz, Y., Ioannou, C. C., Huepe, C., Lutz, M. J., & Couzin, I. D. (2013) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002915 · Cited by 424 · see citing works
Self-citationParticle, kinetic, and hydrodynamic models of swarming
Carrillo, J. A., Fornasier, M., Toscani, G., & Vecil, F. (2010) · Modeling and simulation in science, engineering & technology · doi:10.1007/978-0-8176-4946-3_12 · Cited by 344 · see citing works
A molecular mechanotransduction pathway regulates collective migration of epithelial cells
Das, T., Safferling, K., Rausch, S., Grabe, N., Boehm, H., & Spatz, J. P. (2015) · Nature Cell Biology · doi:10.1038/ncb3115 · Cited by 335 · see citing works
Stewardship of global collective behavior
Bak-Coleman, J. B., Alfano, M., Barfuss, W., Bergstrom, C. T., Centeno, M. A., Couzin, I. D., Donges, J. F., Galesic, M., Gersick, A. S., Jacquet, J., et al. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2025764118 · Cited by 289 · see citing works
Self-citationFrom behavioural analyses to models of collective motion in fish schools
Lopez, U., Jacques Gautrais, A., Couzin, I. D., & Guy Theraulaz, A. (2012) · Interface Focus · doi:10.1098/rsfs.2012.0033 · Cited by 278 · see citing works
Self-citationOutdoor flocking and formation flight with autonomous aerial robots
Vásárhelyi, G., Viragh, C., Somorjai, G. A., Tarcai, N., Szörényi, T., Nepusz, T., & Vicsek, T. (2014) · IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros.2014.6943105 · Cited by 269 · see citing works
Temporal dynamics and network analysis
Blonder, B., Wey, T. W., Dornhaus, A., James, R., & Sih, A. (2012) · Methods in Ecology and Evolution · doi:10.1111/j.2041-210x.2012.00236.x · Cited by 254 · see citing works
Sepúlveda, N., Petitjean, L., Cochet‐Escartin, O., Grasland‐Mongrain, E., Silberzan, P., & Hakim, V. (2013) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002944 · Cited by 240 · see citing works
STOCHASTIC MEAN-FIELD LIMIT: NON-LIPSCHITZ FORCES AND SWARMING
Bolley, F., Cañizo, J. A., & Carrillo, J. A. (2011) · Mathematical Models and Methods in Applied Sciences · doi:10.1142/s0218202511005702 · Cited by 215 · see citing works
Understanding how animal groups achieve coordinated movement
Herbert‐Read, J. E. (2016) · Journal of Experimental Biology · doi:10.1242/jeb.129411 · Cited by 207 · see citing works
Flocking algorithm for autonomous flying robots
Virágh, C., Vásárhelyi, G., Tarcai, N., Szörényi, T., Somorjai, G., Nepusz, T., & Vicsek, T. (2014) · Bioinspiration & Biomimetics · doi:10.1088/1748-3182/9/2/025012 · Cited by 201 · see citing works
The Best-of-n Problem in Robot Swarms: Formalization, State of the Art, and Novel Perspectives
Valentini, G., Ferrante, E., & Dorigo, M. (2017) · Frontiers in Robotics and AI · doi:10.3389/frobt.2017.00009 · Cited by 195 · see citing works
Pezzulo, G., & Levin, M. G. (2015) · Integrative Biology · doi:10.1039/c5ib00221d · Cited by 167 · see citing works
How perceived threat increases synchronization in collectively moving animal groups
Bode, N. W. F., Faria, J. J., Franks, D. W., Krause, J., & Wood, A. J. (2010) · Proceedings of the Royal Society B: Biological Sciences · doi:10.1098/rspb.2010.0855 · Cited by 154 · see citing works
Locust Collective Motion and Its Modeling
Ariel, G., & Ayali, A. (2015) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1004522 · Cited by 146 · see citing works
Noise-induced schooling of fish
Jhawar, J., Morris, R. G., Amith-Kumar, U. R., Danny Raj, M., Rogers, T., Rajendran, H., & Guttal, V. (2020) · Nature Physics · doi:10.1038/s41567-020-0787-y · Cited by 144 · see citing works
Fornasier, M., & Solombrino, F. (2014) · ESAIM Control Optimisation and Calculus of Variations · doi:10.1051/cocv/2014009 · Cited by 144 · see citing works
Colloquium: Fractional calculus view of complexity: A tutorial
West, B. J. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.1169 · Cited by 143 · see citing works
From Molecules to Management: Mechanisms and Consequences of Locust Phase Polyphenism
Cullen, D. A., Cease, A., Latchininsky, A. V., Ayali, A., Berry, K., Buhl, C., Keyser, R. D., Foquet, B., Hadrich, J. C., Matheson, T., et al. (2017) · Advances in insect physiology · doi:10.1016/bs.aiip.2017.06.002 · Cited by 140 · see citing works
Self-citationA Kinetic Flocking Model with Diffusion
Duan, R., Fornasier, M., & Toscani, G. (2010) · Communications in Mathematical Physics · doi:10.1007/s00220-010-1110-z · Cited by 136 · see citing works
Some Causes of the Variable Shape of Flocks of Birds
Hemelrijk, C. K., & Hildenbrandt, H. (2011) · PLoS ONE · doi:10.1371/journal.pone.0022479 · Cited by 133 · see citing works
Locust Dynamics: Behavioral Phase Change and Swarming
Topaz, C. M., D'Orsogna, M. R., Leah Edelstein-keshet, A., & Bernoff, A. J. (2012) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002642 · Cited by 128 · see citing works
Migration of cells in a social context
Vedel, S., Tay, S., Johnston, D. M., Bruus, H., & Quake, S. R. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1204291110 · Cited by 113 · see citing works
Sparse stabilization and control of alignment models
Caponigro, M., Fornasier, M., Piccoli, B., & Trélat, E. (2014) · Mathematical Models and Methods in Applied Sciences · doi:10.1142/s0218202515400059 · Cited by 113 · see citing works
Control to Flocking of the Kinetic Cucker--Smale Model
Piccoli, B., Rossi, F., & Trélat, E. (2015) · SIAM Journal on Mathematical Analysis · doi:10.1137/140996501 · Cited by 108 · see citing works
Sparse stabilization and optimal control of the Cucker-Smale model
Caponigro, M., C. N. D. A. E. M., Fornasier, M., Piccoli, B., Trélat, E., T. U. M., & U. P. E. M. C. (. P. 6. A. I. U. D. F. A. T. G. I. S. (2013) · Mathematical Control and Related Fields · doi:10.3934/mcrf.2013.3.447 · Cited by 109 · see citing works
Nonparametric inference of interaction laws in systems of agents from trajectory data
Lu, F., Ming, Z., Tang, S., & Maggioni, M. (2019) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1822012116 · Cited by 96 · see citing works
Cues and decision rules in animal migration
Bauer, S., Nolet, B. A., Giske, J., Chapman, J. W., Åkesson, S., Hedenström, A., & Fryxell, J. M. (2011) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199568994.003.0006 · Cited by 99 · see citing works
Collective motion in an active suspension of Escherichia coli bacteria
Gachelin, J., Rousselet, A., Lindner, A., & Clément, É. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/2/025003 · Cited by 98 · see citing works
Albi, G., Choi, Y.-P., Fornasier, M., & Dante Kalise, B. (2017) · Applied Mathematics & Optimization · doi:10.1007/s00245-017-9429-x · Cited by 91 · see citing works
Pruitt, J. N., Grinsted, L., & Settepani, V. (2013) · Animal Behaviour · doi:10.1016/j.anbehav.2013.05.030 · Cited by 90 · see citing works
RetractedDetermining interaction rules in animal swarms
Eriksson, A., Jacobi, M. N., Nyström, J., & Tunstrøm, K. (2010) · Behavioral Ecology · doi:10.1093/beheco/arq118 · Cited by 84 · see citing works
Collective behavior of inanimate boats
Suematsu, N. J., Nakata, S., Awazu, A., & Nishimori, H. (2010) · Physical Review E · doi:10.1103/physreve.81.056210 · Cited by 84 · see citing works
Binary Interaction Algorithms for the Simulation of Flocking and Swarming Dynamics
Albi, G., & Pareschi, L. (2013) · Multiscale Modeling and Simulation · doi:10.1137/120868748 · Cited by 83 · see citing works
Flocking estimates for the Cucker–Smale model with time lag and hierarchical leadership
Pignotti, C., & Vallejo, I. R. (2018) · Journal of Mathematical Analysis and Applications · doi:10.1016/j.jmaa.2018.04.070 · Cited by 80 · see citing works
Emergence of Oblong School Shape: Models and Empirical Data of Fish
Hemelrijk, C. K., Hildenbrandt, H., Reinders, J., & Stamhuis, E. J. (2010) · Ethology · doi:10.1111/j.1439-0310.2010.01818.x · Cited by 80 · see citing works
Adaptive-network models of swarm dynamics
Huepe, C., Zschaler, G., Do, A.-L., & Gross, T. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/7/073022 · Cited by 79 · see citing works
Spontaneous dyadic behavior predicts the emergence of interpersonal neural synchrony
Koul, A., Ahmar, D., Iannetti, G. D., & Novembre, G. (2023) · NeuroImage · doi:10.1016/j.neuroimage.2023.120233 · Cited by 75 · see citing works
Mean-field optimal control as Gamma-limit of finite agent controls
Fornasier, M., Lisini, S., Orrieri, C., & Savaré, G. (2019) · European Journal of Applied Mathematics · doi:10.1017/s0956792519000044 · Cited by 68 · see citing works
Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics
Degond, P., Frouvelle, A., & Liu, J.-G. (2014) · Archive for Rational Mechanics and Analysis · doi:10.1007/s00205-014-0800-7 · Cited by 72 · see citing works
Frouvelle, A. (2012) · Mathematical Models and Methods in Applied Sciences · doi:10.1142/s021820251250011x · Cited by 66 · see citing works
Lévy walk process in self-organization of pedestrian crowds
Murakami, H., Feliciani, C., & Nishinari, K. (2019) · Journal of The Royal Society Interface · doi:10.1098/rsif.2018.0939 · Cited by 64 · see citing works
Multi-scale Inference of Interaction Rules in Animal Groups Using Bayesian Model Selection
Mann, R. P., Perna, A., Strömbom, D., Garnett, R., Herbert‐Read, J. E., Sumpter, D. J. T., & Ward, A. J. W. (2013) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002961 · Cited by 60 · see citing works
Self-citationSwarming and pattern formation due to selective attraction and repulsion
Romańczuk, P., & Schimansky-Geier, L. (2012) · Interface Focus · doi:10.1098/rsfs.2012.0030 · Cited by 60 · see citing works
Collective foraging in spatially complex nutritional environments
Lihoreau, M., Charleston, M., Senior, A. M., Clissold, F. J., Raubenheimer, D., Simpson, S. J., & Buhl, C. (2017) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2016.0238 · Cited by 56 · see citing works
Self-citationFish in a ring: spatio-temporal pattern formation in one-dimensional animal groups
Abaid, N., & Porfiri, M. (2010) · Journal of The Royal Society Interface · doi:10.1098/rsif.2010.0175 · Cited by 59 · see citing works
Group structure in locust migratory bands
Buhl, C., Sword, G. A., Clissold, F. J., & Simpson, S. J. (2010) · Behavioral Ecology and Sociobiology · doi:10.1007/s00265-010-1041-x · Cited by 58 · see citing works
Self-citationAriel, G., Ophir, Y., Levi, S., Ben‐Jacob, E., & Ayali, A. (2014) · PLoS ONE · doi:10.1371/journal.pone.0101636 · Cited by 57 · see citing works
Collective behaviour across animal species
Lellis, P. D., Polverino, G., Ustuner, G., Abaid, N., Macrı̀, S., Bollt, E. M., & Porfiri, M. (2014) · Scientific Reports · doi:10.1038/srep03723 · Cited by 57 · see citing works
Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics
Degond, P., Frouvelle, A., & Liu, J. (2013) · Base Institutionnelle de Recherche de l'université Paris-Dauphine (BIRD) (University Paris-Dauphine) · Cited by 57 · see citing works
Hamann, H. (2013) · Swarm Intelligence · doi:10.1007/s11721-013-0080-0 · Cited by 56 · see citing works
Collective motion with anticipation: Flocking, spinning, and swarming
Morin, A., Caussin, J.-B., Eloy, C., & Bartolo, D. (2015) · Physical Review E · doi:10.1103/physreve.91.012134 · Cited by 54 · see citing works
Making noise: Emergent stochasticity in collective motion
Bode, N. W. F., Franks, D. W., & Wood, A. J. (2010) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2010.08.034 · Cited by 52 · see citing works
Schellinck, J., & White, T. (2011) · Ecological Modelling · doi:10.1016/j.ecolmodel.2011.03.013 · Cited by 48 · see citing works
Inference of Causal Information Flow in Collective Animal Behavior
Lord, W. M., Sun, J., Ouellette, N. T., & Bollt, E. M. (2016) · IEEE Transactions on Molecular Biological and Multi-Scale Communications · doi:10.1109/tmbmc.2016.2632099 · Cited by 51 · see citing works
Efficient spatial coverage by a robot swarm based on an ant foraging model and the Lévy distribution
Schroeder, A. M., Ramakrishnan, S., Kumar, M., & Trease, B. P. (2017) · Swarm Intelligence · doi:10.1007/s11721-017-0132-y · Cited by 51 · see citing works
Rieucau, G., Holmin, A. J., Castillo, J. C., Couzin, I. D., & Handegard, N. O. (2016) · Animal Behaviour · doi:10.1016/j.anbehav.2016.05.002 · Cited by 50 · see citing works
Self-citationBiological active matter aggregates: Inspiration for smart colloidal materials
Vernerey, F. J., Benet, È. S. O. L. À., Blue, L. M., Fajrial, A. K., Sridhar, S. L., Lum, J. S., Shakya, G., Song, K.-H., Thomas, A., & Borden, M. A. (2018) · Advances in Colloid and Interface Science · doi:10.1016/j.cis.2018.11.006 · Cited by 48 · see citing works
Inherent noise appears as a Lévy walk in fish schools
Murakami, H., Niizato, T., Tomaru, T., Nishiyama, Y., & Gunji, Y. (2015) · Scientific Reports · doi:10.1038/srep10605 · Cited by 47 · see citing works
Fractional calculus ties the microscopic and macroscopic scales of complex network dynamics
West, B. J., Turalska, M., & Paolo Grigolini, A. (2014) · University of North Texas Digital Library (University of North Texas) · Cited by 46 · see citing works
Overriding native cell coordination enhances external programming of collective cell migration
Shim, G., Devenport, D., & Cohen, D. J. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2101352118 · Cited by 40 · see citing works
Uncertainty Quantification in Control Problems for Flocking Models
Albi, G., Pareschi, L., & Zanella, M. (2015) · Mathematical Problems in Engineering · doi:10.1155/2015/850124 · Cited by 45 · see citing works
Franks, N. R., Richardson, T. O., Stroeymeyt, N., Kirby, R. W., Amos, W. M. D., Hogan, P. M., Marshall, J. A. R., & Schlegel, T. (2013) · Animal Behaviour · doi:10.1016/j.anbehav.2013.03.010 · Cited by 41 · see citing works
Comportamiento colectivo de animales “swarming” y patrones complejos
Cañizo, J. A., Rosado, J., & Carrillo, J. A. (2010) · Arbor · doi:10.3989/arbor.2010.746n1252 · Cited by 42 · see citing works
Role of committed minorities in times of crisis
Turalska, M., West, B. J., & Paolo Grigolini, A. (2013) · Scientific Reports · doi:10.1038/srep01371 · Cited by 40 · see citing works
Impact of correlated noise in an energy depot model
Zeng, C., Zeng, J., Liu, F., & Wang, H. (2016) · Scientific Reports · doi:10.1038/srep19591 · Cited by 40 · see citing works
Sparse Control of Hegselmann--Krause Models: Black Hole and Declustering
Piccoli, B., Duteil, N. P., & Trélat, E. (2019) · SIAM Journal on Control and Optimization · doi:10.1137/18m1168911 · Cited by 40 · see citing works
Escape rate of an active Brownian particle over a potential barrier
Burada, P. S., & Lindner, B. (2012) · Physical Review E · doi:10.1103/physreve.85.032102 · Cited by 40 · see citing works
Going from microscopic to macroscopic on nonuniform growing domains
Yates, C. A., Baker, R. E., Radek Erban, A., & Maini, P. K. (2012) · Physical Review E · doi:10.1103/physreve.86.021921 · Cited by 38 · see citing works
Self-citationInteraction Network, State Space, and Control in Social Dynamics
Aydoğdu, A., Caponigro, M., McQuade, S. T., Piccoli, B., Duteil, N. P., Rossi, F., & Trélat, E. (2017) · Modeling and simulation in science, engineering & technology · doi:10.1007/978-3-319-49996-3_3 · Cited by 38 · see citing works
Kruk, N., MAISTRENKO, Y. L., & Koeppl, H. (2018) · Physical review. E · doi:10.1103/physreve.98.032219 · Cited by 38 · see citing works
Cox process representation and inference for stochastic reaction–diffusion processes
Schnoerr, D., Grima, R., & Sanguinetti, G. (2016) · Nature Communications · doi:10.1038/ncomms11729 · Cited by 37 · see citing works
Collective Behaviors Through Social Interactions in Bird Flocks
Wang, X., & Lü, J. (2019) · IEEE Circuits and Systems Magazine · doi:10.1109/mcas.2019.2924507 · Cited by 36 · see citing works
Coherent collective behaviour emerging from decentralised balancing of social feedback and noise
Rausch, I., Reina, A., Simoens, P., & Khaluf, Y. (2019) · Swarm Intelligence · doi:10.1007/s11721-019-00173-y · Cited by 36 · see citing works
Emergent Runaway into an Avoidance Area in a Swarm of Soldier Crabs
Murakami, H., Tomaru, T., Nishiyama, Y., Moriyama, T., Niizato, T., & Gunji, Y.-P. (2014) · PLoS ONE · doi:10.1371/journal.pone.0097870 · Cited by 36 · see citing works
Sun, Y., & Lin, W. J. (2015) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4929496 · Cited by 35 · see citing works
Patterns, transitions and the role of leaders in the collective dynamics of a simple robotic flock
Tarcai, N., Virágh, C., Ábel, D., Nagy, M., Várkonyi, P. L., Vásárhelyi, G., & Vicsek, T. (2011) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2011/04/p04010 · Cited by 35 · see citing works
A constrained approach to multiscale stochastic simulation of chemically reacting systems
Cotter, S. L., Zygalakis, K. C., Kevrekidis, I. G., & Radek Erban, A. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3624333 · Cited by 35 · see citing works
Self-citationTopologically induced swarming phase transition on a 2D percolated lattice
Quint, D. A., & Ajay Gopinathan, A. (2015) · Physical Biology · doi:10.1088/1478-3975/12/4/046008 · Cited by 35 · see citing works
Mean-field theory of collective motion due to velocity alignment
Romańczuk, P., & Schimansky-Geier, L. (2011) · Ecological Complexity · doi:10.1016/j.ecocom.2011.07.008 · Cited by 35 · see citing works
Li, W. (2015) · Scientific Reports · doi:10.1038/srep13603 · Cited by 34 · see citing works
Noise-enhanced stability and double stochastic resonance of active Brownian motion
Zeng, C., Zhang, C., Zeng, J., Liu, R., & Wang, H. (2015) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2015/08/p08027 · Cited by 34 · see citing works
Ried, K., Müller, T., & Briegel, H. J. (2019) · PLoS ONE · doi:10.1371/journal.pone.0212044 · Cited by 34 · see citing works
Khaluf, Y., Pinciroli, C., Valentini, G., & Hamann, H. (2017) · Swarm Intelligence · doi:10.1007/s11721-017-0137-6 · Cited by 31 · see citing works
Rieucau, G., Robertis, A. D., Boswell, K. M., & Handegard, N. O. (2014) · Journal of Fish Biology · doi:10.1111/jfb.12520 · Cited by 30 · see citing works
Angle restriction enhances synchronization of self-propelled objects
Gao, J., Havlin, S., Xu, X., & Stanley, E. (2011) · Physical Review E · doi:10.1103/physreve.84.046115 · Cited by 30 · see citing works
Devaine, M., & Jean Daunizeau, A. (2017) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005422 · Cited by 30 · see citing works
Finding continuity and discontinuity in fish schools via integrated information theory
Niizato, T., Sakamoto, K., Mototake, Y.-I., Murakami, H., Tomaru, T., Hoshika, T., & Fukushima, T. (2020) · PLoS ONE · doi:10.1371/journal.pone.0229573 · Cited by 29 · see citing works
Onset of collective motion in locusts is captured by a minimal model
Dyson, L., Yates, C. A., Buhl, C., & McKane, A. J. (2015) · Physical Review E · doi:10.1103/physreve.92.052708 · Cited by 29 · see citing works
Self-citationStochastic cycle selection in active flow networks
Woodhouse, F. G., Forrow, A., Fawcett, J. B., & Dunkel, J. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1603351113 · Cited by 29 · see citing works
Langevin Equations for Reaction-Diffusion Processes
Benitez, F., Duclut, C., Chaté, H., Delamotte, B., Dornic, I., & Muñoz, M. A. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.100601 · Cited by 28 · see citing works
Discrete and continuous models for tissue growth and shrinkage
Yates, C. A. (2014) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2014.01.041 · Cited by 28 · see citing works
Self-citationAdaptive-network models of collective dynamics
Zschaler, G. (2012) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2012-01648-5 · Cited by 28 · see citing works
Finite‐time flocking problem of a Cucker–smale‐type self‐propelled particle model
Han, Y., Zhao, D., & Sun, Y. (2015) · Complexity · doi:10.1002/cplx.21747 · Cited by 28 · see citing works
Pohl, O., Hintsche, M., Alirezaeizanjani, Z., Seyrich, M., Beta, C., & Stark, H. (2017) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005329 · Cited by 28 · see citing works
Fractional calculus ties the microscopic and macroscopic scales of complex network dynamics
West, B. J., Turalska, M., & Grigolini, P. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/4/045009 · Cited by 27 · see citing works
Polansky, L., & Wittemyer, G. (2010) · Journal of The Royal Society Interface · doi:10.1098/rsif.2010.0389 · Cited by 26 · see citing works
- Authors
- Yates, C. A., Erban, R., Escudero, C., Couzin, I. D., Buhl, C., Kevrekidis, I. G., Maini, P. K., & Sumpter, D. J. T.
- Affiliations
- Centre for Mathematical Biology and
- Consejo Superior de Investigaciones Científicas (ES)
- Princeton University (US)
- The University of Sydney (AU)
- University of Oxford (GB)
- Uppsala University (SE)
- ORCID
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2009-04-07
- Volume
- 106
- Issue
- 14
- Pages
- 5464-5469
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC2667078
- OpenAlex
- W2055256257
- Cited by
- 304
- References
- 27
- Citations by year
- 2026: 6 · 2025: 13 · 2024: 15 · 2023: 12 · 2022: 19 · 2021: 13 · 2020: 15 · 2019: 17 · 2018: 20 · 2017: 21 · 2016: 16 · 2015: 23 · 2014: 28 · 2013: 19 · 2012: 28
- FWCI
- 29.02
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Oxford University Research Archive (ORA) (University of Oxford) (acceptedVersion)
- DIGITAL.CSIC (Spanish National Research Council (CSIC)) (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology) (submittedVersion)
- Funders
- Princeton University
- King Abdullah University of Science and Technology (KUK‐C1‐013‐04)
- Directorate for Biological Sciences
- Engineering and Physical Sciences Research Council
- Biotechnology and Biological Sciences Research Council
- Air Force Office of Scientific Research
- Topics
- Physical Sciences › Computer Science › Computer Networks and Communications › Distributed Control Multi-Agent Systems
- Physical Sciences › Engineering › Ocean Engineering › Evacuation and Crowd Dynamics
- Physical Sciences › Engineering › Mechanical Engineering › Modular Robots and Swarm Intelligence
- Keywords
- collective motion, locusts, Sturnidae, directional switching, self-propelled particle model, Fokker-Planck equation, noise, group density, marching bands, animal collective behavior
- MeSH terms
- Animals, Computer Simulation, Flight, Animal, Grasshoppers, Models, Biological, Movement, Noise, Starlings
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
