Corpus ID: 235254255

Asymptotic behavior of the linear consensus model with delay and anticipation

@inproceedings{Haskovec2021AsymptoticBO,
  title={Asymptotic behavior of the linear consensus model with delay and anticipation},
  author={Jan Haskovec},
  year={2021}
}
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 transmissiontype and reaction-type delay that are motivated by modeling inputs. Studying the simplified case of two agents, we show that, depending on the parameter regime, anticipation may have both a stabilizing and destabilizing effect on the solutions. In particular, we demonstrate numerically that… Expand

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References

SHOWING 1-10 OF 39 REFERENCES
Consensus under communication delays
TLDR
This paper assumes that each agent receives instantaneously its own state information but receives the state information from its neighbors after a constant delay, and derives an analytic expression of the consensus equilibrium which depends on the delay and on the initial conditions taken in an interval. Expand
Consensus of the Hegselmann–Krause opinion formation model with time delay
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 suitableExpand
Convergence to consensus for a Hegselmann-Krause-type model with distributed time delay
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 resultExpand
Clustering and asymptotic behavior in opinion formation
Abstract We investigate the long time behavior of models of opinion formation. We consider the case of compactly supported interactions between agents which are also non-symmetric, including forExpand
Feedback Stabilization of First Order Neutral Delay Systems Using the Lambert W Function
This paper presents a new approach to stabilize the first order neutral delay differential systems with two time delays. First, we provided a few oscillation and non-oscillation criteria for theExpand
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. Expand
Consensus over directed static networks with arbitrary finite communication delays.
  • J. Lu, D. Ho, J. Kurths
  • Computer Science, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
TLDR
One well-informed leader is proved to be enough for the regulation of all nodes' final states, even when the external signal is very weak, in directed static networks with arbitrary finite communication delays. Expand
Collective motion patterns of swarms with delay coupling: Theory and experiment.
TLDR
This paper model and experimentally realize a mixed-reality large-scale swarm of delay-coupled agents, assuming agents communicating over an Erdös-Renyi network, and demonstrates the existence of stable coherent patterns that can be achieved only with delay coupling and that are robust to decreasing network connectivity and heterogeneity in agent dynamics. Expand
A simple proof of the continuous time linear consensus problem with applications in non-linear flocking networks
TLDR
The linear distributed consensus problem in continuous time is revisited, to provide a simple and elegant proof under very mild assumptions, based on a novel extension of the contraction coefficient that can be adapted to the continuous time version of the model. Expand
Flocking and asymptotic velocity of the Cucker–Smale model with processing delay
Abstract The processing delay is incorporated into the influence function of the well-known Cucker–Smale model for self-organized systems with multiple agents. Both symmetric and non-symmetricExpand
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