Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Active Particles, Volume 2Kinetic Models for Pattern Formation in Animal Aggregations: A Symmetry and Bifurcation Approach

Active Particles, Volume 2: Kinetic Models for Pattern Formation in Animal Aggregations: A... [In this study we start by reviewing a class of 1D hyperbolic/kinetic models (with two velocities) used to investigate the collective behaviour of cells, bacteria or animals. We then focus on a restricted class of nonlocal models that incorporate various inter-individual communication mechanisms, and discuss how the symmetries of these models impact the various types of spatially heterogeneous and spatially homogeneous equilibria exhibited by these nonlocal models. In particular, we characterise a new type of equilibria that was not discussed before for this class of models, namely a relative equilibria. Then we simulate numerically these models and show a variety of spatio-temporal patterns (including classic equilibria and relative equilibria) exhibited by these models. We conclude by introducing a continuation algorithm (which takes into account the models symmetries) that allows us to track the solutions bifurcating from these different equilibria. Finally, we apply this algorithm to identify a D3-symmetric steady-state solution.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Active Particles, Volume 2Kinetic Models for Pattern Formation in Animal Aggregations: A Symmetry and Bifurcation Approach

Part of the Modeling and Simulation in Science, Engineering and Technology Book Series
Editors: Bellomo, Nicola; Degond, Pierre; Tadmor, Eitan
Buono, Pietro-Luciano; Eftimie, Raluca; Kovacic, Mitchell; van Veen, Lennaert
Active Particles, Volume 2 — Aug 23, 2019
Download PDF
25 pages

Loading next page...
 
/lp/springer-journals/active-particles-volume-2-kinetic-models-for-pattern-formation-in-GZXjqWCTSx
Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2019
ISBN
978-3-030-20296-5
Pages
39 –64
DOI
10.1007/978-3-030-20297-2_2
Publisher site
See Chapter on Publisher Site

Abstract

[In this study we start by reviewing a class of 1D hyperbolic/kinetic models (with two velocities) used to investigate the collective behaviour of cells, bacteria or animals. We then focus on a restricted class of nonlocal models that incorporate various inter-individual communication mechanisms, and discuss how the symmetries of these models impact the various types of spatially heterogeneous and spatially homogeneous equilibria exhibited by these nonlocal models. In particular, we characterise a new type of equilibria that was not discussed before for this class of models, namely a relative equilibria. Then we simulate numerically these models and show a variety of spatio-temporal patterns (including classic equilibria and relative equilibria) exhibited by these models. We conclude by introducing a continuation algorithm (which takes into account the models symmetries) that allows us to track the solutions bifurcating from these different equilibria. Finally, we apply this algorithm to identify a D3-symmetric steady-state solution.]

Published: Aug 23, 2019

There are no references for this article.