caa a22 4500 605514976 CHVBK 20210128100707.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s00205-014-0800-7 doi (NATIONALLICENCE)springer-10.1007/s00205-014-0800-7 Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics [Elektronische Daten] [Pierre Degond, Amic Frouvelle, Jian-Guo Liu] We provide a complete and rigorous description of phase transitions for kinetic models of self-propelled particles interacting through alignment. These models exhibit a competition between alignment and noise. Both the alignment frequency and noise intensity depend on a measure of the local alignment. We show that, in the spatially homogeneous case, the phase transition features (number and nature of equilibria, stability, convergence rate, phase diagram, hysteresis) are totally encoded in how the ratio between the alignment and noise intensities depend on the local alignment. In the spatially inhomogeneous case, we derive the macroscopic models associated to the stable equilibria and classify their hyperbolicity according to the same function. Springer-Verlag Berlin Heidelberg, 2014 Degond Pierre UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, Université de Toulouse, 31062, Toulouse, France aut Frouvelle Amic CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, 75775, Paris Cedex 16, France aut Liu Jian-Guo Department of Physics, Duke University, 27708, Durham, NC, USA aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/1(2015-04-01), 63-115 0003-9527 216:1<63 2015 216 205 https://doi.org/10.1007/s00205-014-0800-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0800-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Degond Pierre UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, Université de Toulouse, 31062, Toulouse, France aut NATIONALLICENCE 700 1- Frouvelle Amic CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, 75775, Paris Cedex 16, France aut NATIONALLICENCE 700 1- Liu Jian-Guo Department of Physics, Duke University, 27708, Durham, NC, USA aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/1(2015-04-01), 63-115 0003-9527 216:1<63 2015 216 205