Abstract
We prove the asymptotic flocking behavior of a general model of swarming dynamics. The model describing interacting particles encompasses three types of behavior: repulsion, alignment and attraction. We refer to this dynamics as the three-zone model. Our result expands the analysis of the so-called Cucker-Smale model where only alignment rule is taken into account. Whereas in the Cucker-Smale model, the alignment should be strong enough at long distance to ensure flocking behavior, here we only require that the attraction is described by a confinement potential. The key for the proof is to use that the dynamics is dissipative thanks to the alignment term which plays the role of a friction term. Several numerical examples illustrate the result and we also extend the proof for the kinetic equation associated with the three-zone dynamics.
Original language | English (US) |
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Pages (from-to) | 7692-7707 |
Number of pages | 16 |
Journal | Mathematical Biosciences and Engineering |
Volume | 17 |
Issue number | 6 |
DOIs | |
State | Published - Nov 5 2020 |
Keywords
- Agent-based models
- Collective-behavior
- Energy estimates
- Flocking
- Kinetic equations
ASJC Scopus subject areas
- Modeling and Simulation
- General Agricultural and Biological Sciences
- Computational Mathematics
- Applied Mathematics