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 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

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  Ιωαννησ Τσιτσικλησ,et al.  PROBLEMS IN DECENTRALIZED DECISION MAKING AND COMPUTATION , 1984 .

[3]  John N. Tsitsiklis,et al.  Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms , 1984, 1984 American Control Conference.

[4]  Mei Han An,et al.  accuracy and stability of numerical algorithms , 1991 .

[5]  B. Mohar.  THE LAPLACIAN SPECTRUM OF GRAPHS y , 1991 .

[6]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[7]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[8]  D. Grünbaum,et al.  From individuals to aggregations: the interplay between behavior and physics. , 1999, Journal of theoretical biology.

[9]  G. F.,et al.  From individuals to aggregations: the interplay between behavior and physics. , 1999, Journal of theoretical biology.

[10]  Michael William Newman,et al.  The Laplacian spectrum of graphs , 2001 .

[11]  Felipe Cucker,et al.  Best Choices for Regularization Parameters in Learning Theory: On the Bias—Variance Problem , 2002, Found. Comput. Math..

[12]  James W. Minett,et al.  Self-organization and selection in the emergence of vocabulary , 2002, Complex..

[13]  George J. Pappas,et al.  Stable flocking of mobile agents, part I: fixed topology , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[14]  George J. Pappas,et al.  Stable flocking of mobile agents part I: dynamic topology , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[15]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[16]  Kevin M. Passino,et al.  Stable social foraging swarms in a noisy environment , 2004, IEEE Transactions on Automatic Control.

[17]  Felipe Cucker,et al.  Modeling Language Evolution , 2004, Found. Comput. Math..

[18]  Reza Olfati-Saber,et al.  Flocking for multi-agent dynamic systems: algorithms and theory , 2006, IEEE Transactions on Automatic Control.