Multi-cluster flocking behavior of the hierarchical Cucker–Smale model

Ru, Lining; Xue, Xiaoping

doi:10.1016/j.jfranklin.2016.12.018

Cited by 23 publications

(7 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We also refer the readers to previous studies [4][5][6] for the emergent flocking behavior of C-S model (1). In recent years, various modifications of the classical C-S model have been investigated; see previous works [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and the references therein. Since each individual usually takes a while to receive environmental information, time delays appear naturally in the C-S models.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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

Liu

Wang

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

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 constructing a new energy functional combined with L2‐analysis, we obtain the uniform bound of particle velocities, and then by establishing a system of dissipative differential inequalities together with L∞‐analysis, we prove the existence of asymptotic flocking solutions when the maximum value of time delays is sufficiently small.

show abstract

Section: Introduction and Main Resultsmentioning

confidence: 99%

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

Liu

Wang

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…In the successive contributions, the nonsymmetric interaction, local interaction weight, and the time lag arguments are all incorporated in the more general model settings. For more detailed discussions, we refer the readers to previous studies 1,2,19‐28 and the references therein. These various literatures imply that the connectedness of the underlying adjacency matrix plays a crucial role in the analysis of synchronization.…”

Section: Introductionmentioning

confidence: 99%

Collective periodic motions in a multiparticle model involving processing delay

Liu

Xiao

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

How to understand the dynamical collective performances is of particular significance in both theories and applications. In this paper, we are interested in investigating the combined influences of local interaction and processing delay on the asymptotic behavior in a particle model with local communication weights. With new observations, we show that the desired particle system undergoes both periodic flocking and periodic clustering behaviors when the processing delay crosses a threshold value and the eigenvalue 1 of average matrix is semi‐simple. In this case, the connectedness of the particle system may be absent. Also, the number of clusters is discussed by using subspace analysis. In results, some criteria on flocking and clustering emergence with exponential convergent rate are established by the standard functional differential equations analysis when the processing delay is small. When the processing delay reaches the threshold value, the system undergoes periodic flocking and periodic clustering emergence. It also shows that the processing time lags qualitatively change the emergent performances in a nonlinear way. Finally, we conclude this study with several numerical simulations that intuitively illustrate the validity of the theoretical results and address some discussions for both variable communication weight and distributed processing delay.

show abstract

“…The reference [27] considered the influence of the potential leadership of free-will agents on the convergence of the system. The single-cluster (or global) flocking phenomenon of Cucker-Smale model with a leader was extended to a multi-cluster flocking phenomenon for the first time in [28]. Recently, Shi et al examined the leader-follower flocking control of Cucker-Smale model with time-varying heterogeneous delays.…”

Section: Introductionmentioning

confidence: 99%

Cucker-Smale Flocking Control of Leader-Follower Multiagent Systems With Intermittent Communication

2019

View full text Add to dashboard Cite

This paper investigates the Cucker-Smale flocking control problem of leader-follower multiagent systems in the presence of periodic intermittent communication, in which networked agents update the states by communicating with their neighbors during active periods and remain stable during dormancy periods. A distributed update algorithm that relies on the position error between agents is designed. Based on this algorithm, the problem of Cucker-Smale flocking with periodic intermittent communication is first transformed into a convergence problem of infinite products of nonnegative matrices. Then, this convergence problem is theoretically solved by using hybrid tools including nonnegative matrix analysis and graph theory. Finally, a sufficient condition, which relates to the weight function and the period length of intermittent communication is established. Moreover, numerical examples are presented to demonstrate the validity of the theoretical result. INDEX TERMSFlocking control, Cucker-Smale model, multiagent systems, intermittent communication.

show abstract

Multi-cluster flocking behavior of the hierarchical Cucker–Smale model

Cited by 23 publications

References 34 publications

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

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

Collective periodic motions in a multiparticle model involving processing delay

Cucker-Smale Flocking Control of Leader-Follower Multiagent Systems With Intermittent Communication

Contact Info

Product

Resources

About