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

@article{Choi2019EmergentBO, title={Emergent behavior of Cucker-Smale model with normalized weights and distributed time delays}, author={Young-Pil Choi and Cristina Pignotti}, journal={Networks Heterog. Media}, year={2019}, volume={14}, pages={789-804} }

We study a Cucker-Smale-type flocking model with distributed time delay where individuals interact with each other through normalized communication weights. Based on a Lyapunov functional approach, we provide sufficient conditions for the velocity alignment behavior. We then show that as the number of individuals N tends to infinity, the N-particle system can be well approximated by a delayed Vlasov alignment equation. Furthermore, we also establish the global existence of measure-valued…

## 13 Citations

Asymptotic Flocking Behavior of the General Finite-Dimensional Cucker–Smale Model with Distributed Time Delays

- Mathematics
- 2020

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…

Emergence of time‐asymptotic flocking for a general Cucker–Smale‐type model with distributed time delays

- MathematicsMathematical Methods in the Applied Sciences
- 2020

In this paper, we analyze the asymptotic flocking behavior for a Cucker–Smale‐type model with a disturbed delayed coupling, where delays are information processing and reactions of individuals. By…

Convergence to consensus for a Hegselmann-Krause-type model with distributed time delay

- Mathematics
- 2020

In this paper we study a Hegselmann-Krause opinion formation model with distributed time delay and positive influence functions. Through a Lyapunov functional approach, we provide a consensus result…

Controlled pattern formation of stochastic Cucker–Smale systems with network structures

- Mathematics, Computer ScienceCommunications in Nonlinear Science and Numerical Simulation
- 2022

Emergent behaviors of a thermodynamic Cucker‐Smale flock with a time‐delay on a general digraph

- PhysicsMathematical Methods in the Applied Sciences
- 2021

We present emergent flocking dynamics of a thermodynamic Cucker‐Smale (TCS) flock on a general digraph with spanning trees under the effect of communication time‐delays. The TCS model describes a…

Flocking behaviours of a delayed collective model with local rule and critical neighbourhood situation

- MathematicsMath. Comput. Simul.
- 2021

Cucker-Smale model with finite speed of information propagation: well-posedness, flocking and mean-field limit

- Mathematics
- 2021

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…

Consensus of the Hegselmann–Krause opinion formation model with time delay

- MathematicsMathematical Methods in the Applied Sciences
- 2020

In this paper, we study Hegselmann–Krause models with a time‐variable time delay. Under appropriate assumptions, we show the exponential asymptotic consensus when the time delay satisfies a suitable…

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.

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…

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