Flocking with short-range interactions

Abstract

We study the large-time behavior of continuum alignment dynamics based on Cucker-Smale (CS)-type interactions which involve short-range kernels, that is, communication kernels with support much smaller than the diameter of the crowd. We show that if the amplitude of the interactions is larger than a finite threshold, then unconditional hydrodynamic flocking follows. Since we do not impose any regularity nor do we require the kernels to be bounded, the result covers both regular and singular interaction kernels. Moreover, we treat initial densities in the general class of compactly supported measures which are required to have positive mass on average (over balls at small enough scale), but otherwise vacuum is allowed at smaller scales. Consequently, our arguments of hydrodynamic flocking apply, mutatis mutandis, to the agent-based CS model with finitely many Dirac masses. In particular, discrete flocking threshold is shown to depend on the number of dense clusters of communication but otherwise does not grow with the number of agents.

References in corpus (7)

• A new model for self-organized dynamics and its flocking behavior
• Critical thresholds in flocking hydrodynamics\\with nonlocal alignment
• Euler-type equations and commutators in singular and hyperbolic limits of kinetic Cucker-Smale models
• Flocking dynamics and mean-field limit in the Cucker-Smale-type model with topological interactions
• Global regularity for the fractional Euler alignment system
• Eulerian dynamics with a commutator forcing III. Fractional diffusion of order $0<\alpha <1$
• Global existence and stability of nearly aligned flocks

Cited by in corpus (3)

• Cucker-Smale type dynamics of infinitely many individuals with repulsive forces
• Density-induced Consensus Protocol
• Random Feature Models for Learning Interacting Dynamical Systems