Hydrodynamic Cucker-Smale Model with Normalized Communication Weights and Time Delay

@article{Choi2019HydrodynamicCM,
  title={Hydrodynamic Cucker-Smale Model with Normalized Communication Weights and Time Delay},
  author={Young-Pil Choi and Jan Haskovec},
  journal={SIAM J. Math. Anal.},
  year={2019},
  volume={51},
  pages={2660-2685}
}
We study a hydrodynamic Cucker-Smale-type model with time delay in communication and information processing, in which agents interact with each other through normalized communication weights. The model consists of a pressureless Euler system with time delayed non-local alignment forces. We resort to its Lagrangian formulation and prove the existence of its global in time classical solutions. Moreover, we derive a sufficient condition for the asymptotic flocking behavior of the solutions… 
Exponential asymptotic flocking in the Cucker-Smale model with distributed reaction delays.
TLDR
Using backward-forward and stability estimates on the quadratic velocity fluctuations, sufficient conditions are derived for asymptotic flocking of the solutions of the Cucker-Smale system and the applicability of the theory to particular delay distributions is demonstrated.
Cucker-Smale model with finite speed of information propagation: well-posedness, flocking and mean-field limit
We study a variant of the Cucker-Smale model where information between agents propagates with a finite speed c > 0. This leads to a system of functional differential equations with state-dependent
Emergent behavior of Cucker-Smale flocking particles with time delays
We analyze Cucker-Smale flocking particles with delayed coupling, where different constant delays are considered between particles. By constructing a system of dissipative differential inequalities
The global Cauchy problem for compressible Euler equations with a nonlocal dissipation
  • Young-Pil Choi
  • Mathematics
    Mathematical Models and Methods in Applied Sciences
  • 2019
This paper studies the global existence and uniqueness of strong solutions and its large-time behavior for the compressible isothermal Euler equations with a nonlocal dissipation. The system is
Uniform-in-time bound for kinetic flocking models
The delayed Cucker-Smale model with short range communication weights
TLDR
A simple sufficient condition of the initial data to the non-flocking behavior of the delayed Cucker-Smale model is established and a flocking result is obtained, which also depends upon theinitial data in the short range communication case.
Quantifying the hydrodynamic limit of Vlasov-type equations with alignment and nonlocal forces
In this paper, we quantify the asymptotic limit of collective behavior kinetic equations arising in mathematical biology modeled by Vlasov-type equations with nonlocal interaction forces and
Invariance of velocity angles and flocking in the Inertial Spin model
We study the invariance of velocity angles and flocking properties of the Inertial Spin model introduced by Cavagna et al. [J. Stat. Phys., 158, (2015), 601–627]. We present a novel approach, based
Flocking in the Cucker-Smale model with self-delay and nonsymmetric interaction weights
  • J. Haskovec
  • Mathematics
    Journal of Mathematical Analysis and Applications
  • 2022
...
1
2
...

References

SHOWING 1-10 OF 21 REFERENCES
Cucker-Smale model with normalized communication weights and time delay
We study a Cucker-Smale-type system with time delay in which agents interact with each other through normalized communication weights. We construct a Lyapunov functional for the system and provide
Emergent Dynamics for the Hydrodynamic Cucker-Smale System in a Moving Domain
TLDR
The initial value problem with a moving domain is considered to investigate the global existence and time-asymptotic behavior of classical solutions, provided that the initial mass density has bounded support and the initial data are in an appropriate Sobolev space.
A Cucker-Smale Model with Noise and Delay
TLDR
Sufficient conditions for flocking for the generalized Cucker--Smale model are derived by using a suitable Lyapunov functional and a new result regarding the asymptotic behavior of delayed geometric Brownian motion is obtained.
Critical thresholds in flocking hydrodynamics with non-local alignment
  • E. Tadmor, Changhui Tan
  • Mathematics
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2014
TLDR
It is shown that there exist critical thresholds in the phase space of the initial configuration which dictate the global regularity versus a finite-time blow-up, and the regularity of non-local alignment in the presence of vacuum is explored.
A Review on Attractive–Repulsive Hydrodynamics for Consensus in Collective Behavior
This survey summarizes and illustrates the main qualitative properties of hydrodynamics models for collective behavior. These models include a velocity consensus term together with
Critical thresholds in 1D Euler equations with nonlocal forces
We study the critical thresholds for the compressible pressureless Euler equations with pairwise attractive or repulsive interaction forces and non-local alignment forces in velocity in one
On the pressureless damped Euler–Poisson equations with quadratic confinement: Critical thresholds and large-time behavior
We analyze the one-dimensional pressureless Euler–Poisson equations with linear damping and nonlocal interaction forces. These equations are relevant for modeling collective behavior in mathematical
Pressureless Euler alignment system with control
TLDR
The control dynamics is characterized as a sub-optimal approximation to the optimal control problem constrained to the evolution of the pressureless Euler alignment system and the critical thresholds that lead to global regularity or finite-time blow-up of strong solutions in one and two dimensions are discussed.
Emergent dynamics of the Cucker-Smale flocking model and its variants
In this chapter, we present the Cucker–Smale-type flocking models and discuss their mathematical structures and flocking theorems in terms of coupling strength, interaction topologies, and initial
A New Model for Self-organized Dynamics and Its Flocking Behavior
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
...
1
2
3
...