Exponential asymptotic flocking in the Cucker-Smale model with distributed reaction delays.

@article{Haskovec2020ExponentialAF,
  title={Exponential asymptotic flocking in the Cucker-Smale model with distributed reaction delays.},
  author={Jan Haskovec and Ioannis Markou},
  journal={Mathematical biosciences and engineering : MBE},
  year={2020},
  volume={17 5},
  pages={
          5651-5671
        }
}
We study a variant of the Cucker-Smale system with distributed reaction delays. Using backward-forward and stability estimates on the quadratic velocity fluctuations we derive sufficient conditions for asymptotic flocking of the solutions. The conditions are formulated in terms of moments of the delay distribution and they guarantee exponential decay of velocity fluctuations towards zero for large times. We demonstrate the applicability of our theory to particular delay distributions… 

Figures from this paper

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
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.
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
Asymptotic behavior of the linear consensus model with delay and anticipation
  • J. Haskovec
  • Mathematics
    Mathematical Methods in the Applied Sciences
  • 2022
We study asymptotic behavior of solutions of the first-order linear consensus model with delay and anticipation, which is a system of neutral delay differential equations. We consider both the
Flocking in the Cucker-Smale model with self-delay and nonsymmetric interaction weights
  • J. Haskovec
  • Mathematics
    Journal of Mathematical Analysis and Applications
  • 2022

References

SHOWING 1-10 OF 46 REFERENCES
Asymptotic Flocking Behavior of the General Finite-Dimensional Cucker–Smale Model with Distributed Time Delays
In this paper, we study a Cucker–Smale-type flocking model with distributed time delays, in which individuals interact with each other through general communication weights, and delays are
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
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 the
Hydrodynamic Cucker-Smale Model with Normalized Communication Weights and Time Delay
TLDR
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 is studied, showing the presence of a critical phenomenon for the Eulerian system posed in the spatially one-dimensional setting.
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.
Emergent behavior of Cucker-Smale flocking particles with heterogeneous time delays
Complete Cluster Predictability of the Cucker–Smale Flocking Model on the Real Line
TLDR
This paper presents an explicit criterion and algorithm to calculate the number of clusters and their bulk velocities in terms of initial configuration, coupling strength and communication weight function in a one-dimensional setting and presents a finite increasing sequence of coupling strengths in which thenumber of asymptotic clusters has a jump.
Asymptotic Flocking Dynamics for the Kinetic Cucker-Smale Model
TLDR
A continuous analogue of the theorems of [F. Cucker and S. Smale, IEEE Trans. Automat. Control, 52 (2007), pp. 852–862] is shown to hold for the solutions on the kinetic model, which means that the solutions will concentrate exponentially fast in velocity to the mean velocity of the initial condition, while in space they will converge towards a translational flocking solution.
Convergence to consensus of the general finite-dimensional Cucker-Smale model with time-varying delays
TLDR
The Cucker-Smale model in finite dimension is considered, modelling interacting collective dynamics and their possible evolution to consensus by a Lyapunov functional approach, and convergence results to consensus for symmetric as well as nonsymmetric communication weights under some structural conditions are provided.
...
1
2
3
4
5
...