A simple proof of the Cucker-Smale flocking dynamics and mean-field limit
暂无分享,去创建一个
[1] P. Raviart. An analysis of particle methods , 1985 .
[2] P. Degond,et al. Large Scale Dynamics of the Persistent Turning Walker Model of Fish Behavior , 2007, 0710.4996.
[3] Andrea L. Bertozzi,et al. Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups , 2004, SIAM J. Appl. Math..
[4] D. Helbing. Traffic and related self-driven many-particle systems , 2000, cond-mat/0012229.
[5] W. Rappel,et al. Self-organization in systems of self-propelled particles. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.
[6] Jianhong Shen,et al. Cucker–Smale Flocking under Hierarchical Leadership , 2006, q-bio/0610048.
[7] Vicsek,et al. Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.
[8] Dudley,et al. Real Analysis and Probability: Measurability: Borel Isomorphism and Analytic Sets , 2002 .
[9] Pierre Degond,et al. Macroscopic limit of self-driven particles with orientation interaction , 2007 .
[10] Felipe Cucker,et al. Emergent Behavior in Flocks , 2007, IEEE Transactions on Automatic Control.
[11] H. Spohn. Large Scale Dynamics of Interacting Particles , 1991 .
[12] E. Tadmor,et al. From particle to kinetic and hydrodynamic descriptions of flocking , 2008, 0806.2182.
[13] D. Levy,et al. Particle, kinetic and fluid models for phototaxis , 2009 .
[14] Steven V. Viscido,et al. Self-Organized Fish Schools: An Examination of Emergent Properties , 2002, The Biological Bulletin.
[15] Helmut Neunzert,et al. An introduction to the nonlinear Boltzmann-Vlasov equation , 1984 .
[16] J. Toner,et al. Flocks, herds, and schools: A quantitative theory of flocking , 1998, cond-mat/9804180.
[17] S. Smale,et al. On the mathematics of emergence , 2007 .
[18] Pierre Degond,et al. Continuum limit of self-driven particles with orientation interaction , 2007, 0710.0293.
[19] Maximino Aldana,et al. Phase Transitions in Self-Driven Many-Particle Systems and Related Non-Equilibrium Models: A Network Approach , 2003 .
[20] Paul A. Milewski,et al. A simple model for biological aggregation with asymmetric sensing , 2008 .