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

Choi, Young Pil; Li, Zhuchun

doi:10.1016/j.aml.2018.06.018

Cited by 75 publications

(50 citation statements)

References 12 publications

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“…In the literature, the study on the C-S type models with time-delay is all restricted to the special network topologies. In [10,11,20,34], flocking estimates for the C-S type models with time-delay on a complete network have been discussed using Lyapunov type approach. In a recent work [35], the C-S type model with time-delay in velocity component has been also discussed on a hierarchical network where the asymptotic velocities of particles are given by that of leader.…”

Section: Description Of Main Resultsmentioning

confidence: 99%

Interplay of time-delay and velocity alignment in the Cucker-Smale model on a general digraph

Dong¹,

Ha²,

Kim³

2017

Discrete &Amp; Continuous Dynamical Systems - B

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We study dynamic interplay between time-delay and velocity alignment in the ensemble of Cucker-Smale (C-S) particles(or agents) on time-varying networks which are modeled by digraphs containing spanning trees. Time-delayed dynamical systems often appear in mathematical models from biology and control theory, and they have been extensively investigated in literature. In this paper, we provide sufficient frameworks for the mono-cluster flocking to the continuous and discrete C-S models, which are formulated in terms of system parameters and initial data. In our proposed frameworks, we show that the continuous and discrete C-S models exhibit exponential flocking estimates. For the explicit C-S communication weights which decay algebraically, our results exhibit threshold phenomena depending on the decay rate and depth of digraph. We also provide several numerical examples and compare them with our analytical results.

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Section: Description Of Main Resultsmentioning

confidence: 99%

Interplay of time-delay and velocity alignment in the Cucker-Smale model on a general digraph

Dong¹,

Ha²,

Kim³

2017

Discrete &Amp; Continuous Dynamical Systems - B

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“…The case of CS-model with hierarchical leadership and a pointwise time delay has been recently studied by the authors ( [33]). Other models with (pointwise) time delay, without leadership, have been considered in [8,9,28,34], while for other extensions of Shen's results, without delay, we refer to [16,24,27,26,25].…”

Section: Introductionmentioning

confidence: 99%

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

Pignotti

Vallejo

2019

Trends in Control Theory and Partial Differential Equations

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We extend the analysis developed in [33] in order to prove convergence to consensus results for a Cucker-Smale type model with hierarchical leadership and distributed delay. Flocking estimates are obtained for a general interaction potential with divergent tail. We analyze also the model when the ultimate leader can change its velocity. In this case we give a flocking result under suitable conditions on the leader's acceleration.

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“…The CS model has received lots of attention in literature from different perspectives, i.e., global and local flocking [8,18,19,32,34,36], collision avoiding [1,16], time-delay effect [9,10,21,24,27,44], hierarchical and rooted leadership, general digraph [20,38,39,47], application to flight navigation [43], noisy effects [2,17,23,33], mean-field limit [5,32,34], kinetic and hydrodynamic description [6,7,25,36,45], and variants of C-S model [41,42], etc. (see recent survey papers [14,40] for details).…”

Section: Introductionmentioning

confidence: 99%

Emergent behaviors of continuous and discrete thermomechanical Cucker–Smale models on general digraphs

Dong

Kim

2019

Math. Models Methods Appl. Sci.

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We present emergent dynamics of continuous and discrete thermomechanical Cucker-Smale(TCS) models equipped with temperature as an extra observable on general digraph. In previous literature, the emergent behaviors of the TCS models were mainly studied on a complete graph, or symmetric connected graphs. Under this symmetric setting, the total momentum is a conserved quantity. This determines the asymptotic velocity and temperature a priori using the initial data only. Moreover, this conservation law plays a crucial role in the flocking analysis based on the elementary ℓ 2 energy estimates. In this paper, we consider a more general connection topology which is registered by a general digraph, and the weights between particles are given to be inversely proportional to the metric distance between them. Due to this possible symmetry breaking in communication, the total momentum is not a conserved quantity, and this lack of conservation law makes the asymptotic velocity and temperature depend on the whole history of solutions. To circumvent this lack of conservation laws, we instead employ some tools from matrix theory on the scrambling matrices and some detailed analysis on the state-transition matrices. We present two sufficient frameworks for the emergence of mono-cluster flockings on a digraph for the continuous and discrete models. Our sufficient frameworks are given in terms of system parameters and initial data.Definition 1.1. [31, 35] Let C := (X, V, Θ) be a time-dependent configuration on the extended state space R N d × R N d × R d . Then the configuration C exhibits asymptotic mono-cluster flocking, if and only if the following conditions hold: sup 0≤t<∞ D(X(t)) < ∞, lim t→∞ D(V (t)) = 0, lim t→∞ D(Θ(t)) = 0. December 10, 2018 1:46 WSPC/INSTRUCTION FILE

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

Cited by 75 publications

References 12 publications

Interplay of time-delay and velocity alignment in the Cucker-Smale model on a general digraph

Interplay of time-delay and velocity alignment in the Cucker-Smale model on a general digraph

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

Emergent behaviors of continuous and discrete thermomechanical Cucker–Smale models on general digraphs

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