caa a22 4500 445391405 CHVBK 20180317143047.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s10955-011-0285-9 doi (NATIONALLICENCE)springer-10.1007/s10955-011-0285-9 A New Model for Self-organized Dynamics and Its Flocking Behavior [Elektronische Daten] [Sebastien Motsch, Eitan Tadmor] We introduce a model for self-organized dynamics which, we argue, addresses several drawbacks of the celebrated Cucker-Smale (C-S) model. The proposed model does not only take into account the distance between agents, but instead, the influence between agents is scaled in term of their relative distance. Consequently, our model does not involve any explicit dependence on the number of agents; only their geometry in phase space is taken into account. The use of relative distances destroys the symmetry property of the original C-S model, which was the key for the various recent studies of C-S flocking behavior. To this end, we introduce here a new framework to analyze the phenomenon of flocking for a rather general class of dynamical systems, which covers systems with non-symmetric influence matrices. In particular, we analyze the flocking behavior of the proposed model as well as other strongly asymmetric models with "leaders”. The methodology presented in this paper, based on the notion of active sets, carries over from the particle to kinetic and hydrodynamic descriptions. In particular, we discuss the hydrodynamic formulation of our proposed model, and prove its unconditional flocking for slowly decaying influence functions. Springer Science+Business Media, LLC, 2011 Self-organized dynamics nationallicence Flocking nationallicence Active sets nationallicence Kinetic formulation nationallicence Moments nationallicence Hydrodynamic formulation nationallicence Motsch Sebastien Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, 20742, College Park, MD, USA aut Tadmor Eitan Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, 20742, College Park, MD, USA aut Journal of Statistical Physics Springer US; http://www.springer-ny.com 144/5(2011-09-01), 923-947 0022-4715 144:5<923 2011 144 10955 https://doi.org/10.1007/s10955-011-0285-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-011-0285-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Motsch Sebastien Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, 20742, College Park, MD, USA aut NATIONALLICENCE 700 1- Tadmor Eitan Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, 20742, College Park, MD, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 144/5(2011-09-01), 923-947 0022-4715 144:5<923 2011 144 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer