Mathematics – Analysis of PDEs
Scientific paper
2011-02-28
Mathematics
Analysis of PDEs
Scientific paper
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.
Motsch Sébastien
Tadmor Eitan
No associations
LandOfFree
A new model for self-organized dynamics and its flocking behavior does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A new model for self-organized dynamics and its flocking behavior, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A new model for self-organized dynamics and its flocking behavior will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-424457