Cucker–Smale Flocking under Hierarchical Leadership

By Jackie Shen. 2006

304 citations recorded by the source corpus.

A mathematical theory on flocking serves the foundation for several ubiquitous multiagent phenomena in biology, ecology, sensor networks, and economics, as well as social behavior like language emergence and evolution. Directly inspired by the recent fundamental works of Cucker and Smale on the construction and analysis of a generic flocking model, we study the emergent behavior of Cucker–Smale flocking under hierarchical leadership. The rates of convergence towards asymptotically coherent group patterns in different scenarios are established. The consistent convergence towards coherent patterns may well reveal the advantages and necessities of having leaders and leadership in a complex (biological, technological, economic, or social) system with sufficient intelligence.

Subfields: Computer Networks and Communications, Public Health, Environmental and Occupational Health, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/672ffcc1f79487d297f4647eadd75b3f7b8df5ab

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Citations in the corpus

Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system (2009, methodology): “The Cucker-Smale (C-S) particle model is a simple relaxation-type model for an N -particle system that reveals a phase transition depending on the level of communication rates (see [2, 3, 8, 10, 16] for details).”
Particle, kinetic, and hydrodynamic models of swarming (2010, methodology): “This structure and the corresponding behavior of the Cucker–Smale model under these assumptions have been investigated by Shen [60].”
Flocking estimates for the Cucker–Smale model with time lag and hierarchical leadership (2017, methodology): “Then, on the one hand, in the undelayed case, i.e. τ = 0, we extend the result of Shen by considering a general potential of divergent tail.”
On the control through leadership of the Hegselmann–Krause opinion formation model (2015, background): “[3, 6, 14, 17, 30, 33] for results on multi-agent systems with leadership.”
Emergent dynamics of the Cucker-Smale flocking model and its variants (2016, background): “The induction method works quite well for the hierarchical C-S flocking [27, 33, 60], but it cannot deal with the case of state-dependent perturbations.”
From particle to kinetic and hydrodynamic descriptions of flocking (2008, background): “In this section, we briefly review the CuckerSmale’s flocking system in [6, 7, 23], which manifests the time-asymptotic flocking behavior of many particle systems.”
Avoiding Collisions in Flocks (2010, background): “Variations of this basic model can be obtained by adding noise [4], [22], steering towards preferred directions [3], hierarchical leadership [ 18 ], etc.”
A New Model for Self-organized Dynamics and Its Flocking Behavior (2011, unknown): “The starting point for our discussion is the pioneering work of Cucker-Smale, [8, 9], which led to many subsequent studies [3, 6, 14, 15, 16, 23].”
A General Collision-Avoiding Flocking Framework (2011, background): “The model was quickly extended in several directions: to include non-symmetric communication functions [18] or nonlinear velocity couplings [8], to consider infinitely many agents modelled as a fluid [2], [11] to avoid collisions [3], to allow for time delays [1], informed agents with preferred dire”
Asymptotic Flocking Dynamics for the Kinetic Cucker-Smale Model (2010, background): “In the biological context, the emergent behavior of bird flocks, fish schools or bacteria aggregations, among others, is a major research topic in population and behavioral biology and ecology [1, 4, 14, 15, 16, 18, 30, 33, 34].”
Extension of the Cucker-Smale Control Law to Space Flight Formations (2009, background): “Shen [15] extended this model to the case of a flock with hierarchical leadership and considered the scenario in which the flock leader may have a freewill acceleration that tends to zero with time.”
On collision-avoiding initial configurations to Cucker-Smale type flocking models (2012, background): “Cucker-Smale’s flocking estimates were refined and generalized to the kinetic and fluid models in recent literature [1, 2, 4, 5, 6, 7, 8, 9, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 27, 31].”
A simple proof of the Cucker-Smale flocking dynamics and mean-field limit (2009, background): “Comparison with Cucker-Smale’s results.”
Flocking in noisy environments (2007, unknown): “11400 Montevideo URUGUAY e-mail: mordecki@cmat.edu.uy”
Heterophilious Dynamics Enhances Consensus (2013, methodology): “[107], and the follow-up works in [40, 41, 70]; the C-S model [36, 37] and related works in [10, 21, 60, 61, 62, 73, 88, 97]; and the StarFlag project [4, 26, 25, 24].”