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A simple proof of the Cucker-Smale flocking dynamics and mean-field limit
We present a simple proof on the formation of flocking to the Cucker-Smale system based on the explicit construction of a Lyapunov functional. Our results also provide a unified condition on theExpand
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From particle to kinetic and hydrodynamic descriptions of flocking
We discuss the Cucker-Smale's (C-S) particle model for flocking, deriving precise conditions for flocking to occur when pairwise interactions are sufficiently strong long range. We then derive aExpand
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Cucker-Smale Flocking With Inter-Particle Bonding Forces
TLDR
The Cucker-Smale (CS) flocking model is an interacting particle system, in which each particle updates its velocity by adding to it a weighted average of the differences of its velocity with those of other particles, in order to incorporate collision avoidance between agents, and at the same time achieve tighter spatial configurations. Expand
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Emergent Behavior of a Cucker-Smale Type Particle Model With Nonlinear Velocity Couplings
  • S. Ha, T. Ha, J. Kim
  • Mathematics, Computer Science
  • IEEE Transactions on Automatic Control
  • 22 March 2010
TLDR
We present a Cucker-Smale type flocking model with nonlinear velocity couplings, and derive sufficient conditions for the formation of flocking in terms of communication weight and initial spatial, velocity standard deviations. Expand
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On collision-avoiding initial configurations to Cucker-Smale type flocking models
Abstract. We present a class of initial-configurations for the Cucker-Smale flocking type models leading no finite-time collisions between particles. For this class of initial-configurations, theExpand
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Nonlinear functionals of the Boltzmann equation and uniform stability estimates
  • S. Ha
  • Mathematics
  • 1 August 2005
Abstract We present nonlinear functionals measuring physical space variation and L 1 -distance between two classical solutions for the Boltzmann equation with a cut-off inverse power potential. InExpand
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Asymptotic formation and orbital stability of phase-locked states for the Kuramoto model
Abstract We discuss the asymptotic formation and nonlinear orbital stability of phase-locked states arising from the ensemble of non-identical Kuramoto oscillators. We provide an explicit lower boundExpand
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On the complete synchronization of the Kuramoto phase model
Abstract We discuss the asymptotic complete phase–frequency synchronization for the Kuramoto phase model with a finite size N . We present sufficient conditions for initial configurations leading toExpand
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Formation of phase-locked states in a population of locally interacting Kuramoto oscillators
Abstract In this paper, we present an asymptotic formation of phase-locked states from the ensemble of Kuramoto oscillators with a symmetric and connected interaction topology. For a limitedExpand
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Global Existence of Plasma Ion-Sheaths and Their Dynamics
Abstract: When a negative high voltage pulse is applied to a target material immersed in a plasma, a boundary layer (sheath) forms around the target and the motion of cold ions in the plasma isExpand
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