Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Degond, P; Frouvelle, A; Liu, JG

Published Date

  • April 1, 2015

Published In

Volume / Issue

  • 216 / 1

Start / End Page

  • 63 - 115

Electronic International Standard Serial Number (EISSN)

  • 1432-0673

International Standard Serial Number (ISSN)

  • 0003-9527

Digital Object Identifier (DOI)

  • 10.1007/s00205-014-0800-7

Citation Source

  • Scopus