Asymptotic flocking in the Cucker-Smale model with reaction-type delays in the non-oscillatory regime

@article{Haskovec2020AsymptoticFI,
  title={Asymptotic flocking in the Cucker-Smale model with reaction-type delays in the non-oscillatory regime},
  author={Jan Haskovec and Ioannis Markou},
  journal={Kinetic \& Related Models},
  year={2020}
}
We study a variant of the Cucker-Smale system with reaction-type delay. Using novel backward-forward and stability estimates on appropriate quantities we derive sufficient conditions for asymptotic flocking of the solutions. These conditions, although not explicit, relate the velocity fluctuation of the initial datum and the length of the delay. If satisfied, they guarantee monotone decay (i.e., non-oscillatory regime) of the velocity fluctuations towards zero for large times. For the… 
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References

SHOWING 1-10 OF 23 REFERENCES
Emergent Behavior in Flocks
TLDR
The main result shows that when beta<1/2 convergence of the flock to a common velocity is guaranteed, while for betages1/ 2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only.
On the mathematics of emergence
Abstract.We describe a setting where convergence to consensus in a population of autonomous agents can be formally addressed and prove some general results establishing conditions under which such
A collisionless singular Cucker-Smale model with decentralized formation control
TLDR
This work addresses the design of decentralized feedback control laws inducing consensus and prescribed spatial patterns over a singular interacting particle system of Cucker-Smale type by studying consensus emergence, collision-avoidance and formation control features in terms of energy estimates for the closed-loop system.
Asymptotic Analysis of a Cucker–Smale System with Leadership and Distributed Delay
We extend the analysis developed in Pignotti and Reche Vallejo (J Math Anal Appl 464:1313–1332, 2018) [34] in order to prove convergence to consensus results for a Cucker–Smale type model with
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.
Collision-avoiding in the singular Cucker-Smale model with nonlinear velocity couplings
Collision avoidance is an interesting feature of the Cucker-Smale (CS) model of flocking that has been studied in many works, e.g. [1, 2, 4, 6, 7, 20, 21, 22]. In particular, in the case of singular
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.
Emergent behavior of Cucker-Smale flocking particles with heterogeneous time delays
Flocking estimates for the Cucker–Smale model with time lag and hierarchical leadership
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.
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