Emergent Behavior in Flocks

We provide a model (for both continuous and discrete time) describing the evolution of a flock. Our model is parameterized by a constant beta capturing the rate of decay-which in our model is polynomial-of the influence between birds in the flock as they separate in space. Our main result shows that...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 52; no. 5; pp. 852 - 862
Main Authors Cucker, F., Smale, S.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.05.2007
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Applied sciences
Automatic control
Beta
Beta decay
Birds
Computer science; control theory; systems
Computer simulation
Consensus reaching problem
Control theory. Systems
Convergence
Councils
Decay rate
emergence
Evolution
Exact sciences and technology
flocking
Gravity
H infinity control
Marine animals
Mathematical models
Mathematics
Polynomials
Consensus reaching problem
emergence
Discrete time
Collective process
Continuous time
flocking
Modeling
Consensus
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Summary:We provide a model (for both continuous and discrete time) describing the evolution of a flock. Our model is parameterized by a constant beta capturing the rate of decay-which in our model is polynomial-of the influence between birds in the flock as they separate in space. Our main result shows that when beta<1/2 convergence of the flock to a common velocity is guaranteed, while for betages1/2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2007.895842