Flocking in noisy environments

By Felipe Cucker, Ernesto Mordecki. 2007

227 citations recorded by the source corpus.

Abstract In recent years, a number of articles proposed mathematical models for emergent phenomena. This is the case, for instance for the flocking of birds or the schooling of fish. In particular, in [F. Cucker, S. Smale, Emergent behavior in flocks, IEEE Trans. on Autom. Control 52 (2007) 852–862], a model was proposed for flocking and it was proved that under certain conditions on the initial positions and velocities of the birds, flocking occurs. In this paper we modify this model by adding random noise to it. We prove that, under conditions similar to those just mentioned, (nearly) flocking occurs in finite time with a certain confidence.

Subfields: Computer Networks and Communications, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/43ed6e3923abe2ca337e7e76b8247f4db9a48355

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

In Molecular Biology

Citations in the corpus

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].”
Flocking estimates for the Cucker–Smale model with time lag and hierarchical leadership (2017, background): “[15, 17, 27, 37, 40, 46, 50, 52]), stochastic terms ([18, 23, 25]), pedestrian crowds (see [16, 31]), infinite-dimensional kinetic models (see [1, 4, 9, 12, 22, 28, 49]), topological models ([5, 29]), control models (see [6, 10, 11, 43, 51]).”
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”
Emergent Behavior of a Cucker-Smale Type Particle Model With Nonlinear Velocity Couplings (2010, methodology): “Several extensions of the C-S model with internal and external forces have been addressed in [13], [14], and the connection with other mechanical and synchronization models in statistical mechanics was also exploited in [15], [16].”
Fokker–Planck equations in the modeling of socio-economic phenomena (2017, background): “[28, 82, 84] In the biological context, a consistent part of the recent research in population and behavioral biology and ecology has been looking for the emergent behavior of bird flocks, fish schools or bacteria aggregations.[26, 27, 38, 39, 40, 60, 61, 62] Other important examples of emergent beh”
Stochastic consensus over noisy networks with Markovian and arbitrary switches (2010, methodology): “For noisy modelling for flocking, formation and rendezvous, the reader is referred to Barooah and Hespanha (2007), Cucker and Mordecki (2008) and Martínez (2007).”
Stochastic Mean-Field Limit: Non-Lipschitz Forces & Swarming (2010, background): “The asymptotic behavior of the Cucker-Smale system with added noise has been recently considered in [15], and eq.”