Flocking in noisy environments |
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Authors: | Felipe Cucker Ernesto Mordecki |
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Institution: | 1. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong;2. Centro de Matemática, Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400 Montevideo, Uruguay |
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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. |
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