# Flocking estimates for the Cucker–Smale model with time lag and hierarchical leadership

@article{Pignotti2018FlockingEF, title={Flocking estimates for the Cucker–Smale model with time lag and hierarchical leadership}, author={Cristina Pignotti and Irene Reche Vallejo}, journal={Journal of Mathematical Analysis and Applications}, year={2018} }

## 47 Citations

Cucker–Smale flocking under hierarchical leadership with time-delay and a free-will leader

- MathematicsCommunications in Mathematical Sciences
- 2022

. We study the discrete-time Cucker-Smale model under hierarchical leadership with a constant time delay. The overall leader of the flock is assumed to have a free-will acceleration. The strength of…

Asymptotic Analysis of a Cucker–Smale System with Leadership and Distributed Delay

- MathematicsTrends in Control Theory and Partial Differential Equations
- 2019

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…

Cucker-Smale flocking under rooted leadership and time-varying heterogeneous delays

- Computer Science, MathematicsAppl. Math. Lett.
- 2019

On the control of the Hegselmann-Krause model with leadership and time delay

- Mathematics
- 2021

We analyze Hegselmann-Krause opinion formation models with leadership in presence of time delay effects. In particular, we consider a model with pointwise time variable time delay and a model with a…

Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time Delays

- Computer ScienceComplex.
- 2021

The Cucker and Smale model is a well-known flocking model that describes the emergence of flocks based on alignment and the existence of the first-order optimality conditions for a delayed optimal control problem is discussed.

Flocking in a two-agent Cucker-Smale model with large delay

- Mathematics
- 2021

It is rigorously proved that flocking behavior emerges for a large information processing delay, and the relationship between the admissible size of time delay and the system’s parameters and initial data is established.

Emergent behavior of Cucker-Smale model with normalized weights and distributed time delays

- MathematicsNetworks Heterog. Media
- 2019

It is shown that as the number of individuals N tends to infinity, the N-particle system can be well approximated by a delayed Vlasov alignment equation and its large-time asymptotic behavior.

Fixed-Time Flocking Problem of a Cucker–Smale Model

- MathematicsMathematical Problems in Engineering
- 2020

In this paper, we studied a Cucker–Smale model with continuous non-Lipschitz protocol. The methodology presented in the current work is based on the explicit construction of a Lyapunov functional. By…

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

- MathematicsMathematical biosciences and engineering : MBE
- 2020

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.

Emergent behavior of Cucker-Smale flocking particles with heterogeneous time delays

- MathematicsAppl. Math. Lett.
- 2018

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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…