Anticipation breeds alignment

Abstract

We study the large-time behavior of systems driven by radial potentials, which react to anticipated positions, ${\mathbf{x}}^{\tau }(t)=\mathbf{x}(t)+\tau \mathbf{v}(t)$, with anticipation increment $\tau >0$. As a special case, such systems yield the celebrated Cucker-Smale model for alignment, coupled with pairwise interactions. Viewed from this perspective, such anticipated-driven systems are expected to emerge into flocking due to alignment of velocities, and spatial concentration due to confining potentials. We treat both the discrete dynamics and large crowd hydrodynamics, proving the decisive role of anticipation in driving such systems with attractive potentials into velocity alignment and spatial concentration. We also study the concentration effect near equilibrium for anticipated-based dynamics of pair of agents governed by attractive-repulsive potentials.

References in corpus (9)

• Self-organization in systems of self-propelled particles
• The derivation of Swarming models: Mean-Field Limit and Wasserstein distances
• On the Dynamics of Large Particle Systems in the Mean Field Limit
• Critical thresholds in flocking hydrodynamics\\with nonlocal alignment
• Mean Field Limit for Coulomb-Type Flows
• Euler-type equations and commutators in singular and hyperbolic limits of kinetic Cucker-Smale models
• Collective Motion with Anticipation: Flocking, Spinning, and Swarming
• Nonlinear stability of flock solutions in second-order swarming models
• The impact of anticipation in dynamical systems

Cited by in corpus (1)

• Asymptotic behavior and control of a "guidance by repulsion" model