Impacts of time delay on flocking dynamics of a two-agent flock model

Published on May 1, 2019in Communications in Nonlinear Science and Numerical Simulation4.26
· DOI :10.1016/J.CNSNS.2018.10.017
Jianhong Wu106
Estimated H-index: 106
(York University)
Sources
Abstract
Abstract Due to finite information transmission and processing time between agents, delays are inevitable and should therefore be incorporated into flocking modeling. To shed light on understanding the impacts of time delay on the dynamics of flock models, we incorporate a time delay to a two-agent flock model and study its flocking dynamics. When the product of the amplitude of the coupling strength and the time delay is relatively small, necessary and sufficient conditions are established for the two-agent flock model to exhibit flocking. We further show that as the delay increases, transcritical bifurcation and Hopf bifurcation may emerge resulting in rich and complex flocking dynamics.
📖 Papers frequently viewed together
References33
Newest
#1Cristina Pignotti (University of L'Aquila)H-Index: 17
#2Irene Reche Vallejo (University of L'Aquila)H-Index: 2
Abstract We analyze the Cucker–Smale model under hierarchical leadership in presence of a time delay. By using a Lyapunov functional approach and some induction arguments we will prove convergence to consensus for every positive delay τ. We also prove a flocking estimate in the case of a free-will leader. These results seem to point out the advantage of a hierarchical structure in order to contrast time delay effects that frequently appear in real situations.
Source
#1Radek Erban (University of Oxford)H-Index: 33
#2Jan Haskovec (KAUST: King Abdullah University of Science and Technology)H-Index: 14
Last. Yongzheng SunH-Index: 13
view all 3 authors...
A generalization of the Cucker--Smale model for collective animal behavior is investigated. The model is formulated as a system of delayed stochastic differential equations. It incorporates two additional processes which are present in animal decision making, but are often neglected in modeling: (i) stochasticity (imperfections) of individual behavior and (ii) delayed responses of individuals to signals in their environment. Sufficient conditions for flocking for the generalized Cucker--Smale mo...
Source
#1Klementyna Szwaykowska (NRL: United States Naval Research Laboratory)H-Index: 7
#2Ira B. Schwartz (NRL: United States Naval Research Laboratory)H-Index: 34
Last. M. Ani Hsieh (Drexel University)H-Index: 19
view all 6 authors...
The formation of coherent patterns in swarms of interacting self-propelled autonomous agents is a subject of great interest in a wide range of application areas, ranging from engineering and physics to biology. In this paper, we model and experimentally realize a mixed-reality large-scale swarm of delay-coupled agents. The coupling term is modeled as a delayed communication relay of position. Our analyses, assuming agents communicating over an Erdos-Renyi network, demonstrate the existence of st...
Source
#1Dimitri Breda (University of Udine)H-Index: 17
#2Odo Diekmann (University of Udine)H-Index: 52
Last. Rossana VermiglioH-Index: 18
view all 5 authors...
We apply the pseudospectral discretization approach to nonlinear delay models described by delay differential equations, renewal equations, or systems of coupled renewal equations and delay differential equations. The aim is to derive ordinary differential equations and to investigate the stability and bifurcation of equilibria of the original model by available software packages for continuation and bifurcation for ordinary differential equations. Theoretical and numerical results confirm the e...
Source
Jul 28, 2015 in CCC (Chinese Control Conference)
#1Liu Feng (China University of Geosciences)H-Index: 1
#2Yin Xiang (China University of Geosciences)H-Index: 1
Last. O. Wang Hua (BU: Boston University)H-Index: 1
view all 5 authors...
In this paper, the problem of Hopf bifurcation for a swarm model of self-propelled agents in the presence of noise and communication time delay is studied. When the value of delayed communication time passes through a critical value, Hopf bifurcation will occur, where the center of mass undergoes a Hopf bifurcation from steady state to a limit cycle, the swarm is transformed from a misaligned state into an aligned state. Using a mean field model, we prove the existence of bifurcation and gave th...
Source
#1Jérôme Fehrenbach (Institut de Mathématiques de Toulouse)H-Index: 13
#2Jacek Narski (Institut de Mathématiques de Toulouse)H-Index: 10
Last. Pierre Degond (Imperial College London)H-Index: 63
view all 9 authors...
We use the results of a pedestrian tracking experiment to identify a follow-the-leader model for pedestrians walking-in-line. We demonstrate the existence of a time-delay between a subject's response and the predecessor's corresponding behavior. This time-delay induces an instability which can be damped out by a suitable relaxation. By comparisons with the experimental data, we show that the model reproduces well the emergence of large-scale structures such as congestions waves. The resulting mo...
Source
#1Bernát Wiandt (BME: Budapest University of Technology and Economics)H-Index: 4
#2Andras Kokuti (BME: Budapest University of Technology and Economics)H-Index: 4
Last. Vilmos Simon (BME: Budapest University of Technology and Economics)H-Index: 24
view all 3 authors...
Today more and more attention is given to collective movement of dynamic nodes, called flocking. The main problem is how to control the nodes to behave as a group and make them move together to destinations (and moreover complete some tasks such as sensing, transporting, etc.). Currently there are many works, which attempt to solve the flocking problem, but very few of them are suitable for real world use. This is because most of the algorithms are overlooking crucial physical limitations or the...
Source
#1Seung-Yeal Ha (SNU: Seoul National University)H-Index: 33
#2Kyoung-Kuk Kim (KAIST)H-Index: 8
Last. Kiseop Lee (University of Louisville)H-Index: 7
view all 3 authors...
We present a new mathematical model for multi-name credit that employs stochastic flocking. Flocking mechanisms have been used in a variety of models of biological, sociological and physical aggregation phenomena. As a direct application of a flocking mechanism, we introduce a credit risk model based on community flocking for a credit worthiness index. Correlations between different credit worthiness indices are explained in terms of communication rates and coupling strengths from the flocking s...
Source
#1Christoforos Somarakis (UMD: University of Maryland, College Park)H-Index: 9
#2John S. Baras (UMD: University of Maryland, College Park)H-Index: 57
Abstract This work studies a class of linear first order and non-linear second order static distributed consensus networks with time-varying multiple propagation delays, in continuous time. We provide conditions for convergence of to a common constant value, under an increased connectivity condition. The results are delay-independent in the sense that they hold for arbitrary bounded delays. Our approach makes use of fundamental concepts from the Non-Negative Matrix Theory in a fairly elementary ...
Source
#1Sebastien MotschH-Index: 16
#2Eitan Tadmor (ASU: Arizona State University)H-Index: 72
We review a general class of models for self-organized dynamics based on alignment. The dynamics of such systems is governed solely by interactions among individuals or “agents,” with the tendency to adjust to their “environmental averages.” This, in turn, leads to the formation of clusters, e.g., colonies of ants, flocks of birds, parties of people, rendezvous in mobile networks, etc. A natural question which arises in this context is to ask when and how clusters emerge through the self-alignme...
Source
Cited By19
Newest
#1Jianfei Cheng (National University of Defense Technology)
#2Lining Ru (Suzhou University of Science and Technology)H-Index: 1
Last. Yicheng Liu (National University of Defense Technology)H-Index: 1
view all 4 authors...
Abstract null null By introducing an attractive-repulsive force in Cucker-Smale model, the dynamic behaviour of multi-agent system is studied. The Cucker-Smale-type model considered in this paper has three properties: collision-avoidance, aggregation and velocity-matching, which are significant rules in dynamic behaviour of multi-agent systems. Results of collision-avoidance, flocking and swarming are given respectively. Different from previous work, the Cucker-Smale-type model shows uncondition...
Source
#1Maoli Chen (National University of Defense Technology)
#2Yicheng Liu (National University of Defense Technology)
We investigate the effect of noise on the emergence of flocking in a coupled systems by constructing a second-order coupled dynamics model, in which the inter-subgroup interaction is affected by ex...
Source
#1Yicheng Liu (National University of Defense Technology)H-Index: 3
#2Jun Wu (CCSU: Changsha University)H-Index: 2
Last. Xiao Wang (National University of Defense Technology)H-Index: 1
view all 3 authors...
Source
#1Jianfei Cheng (National University of Defense Technology)H-Index: 1
#2Zhuchun Li (HIT: Harbin Institute of Technology)H-Index: 1
Last. Jianhong Wu (York University)H-Index: 1
view all 3 authors...
Source
As we known, it is popular for a designed system to achieve a prescribed performance, which have remarkable capability to regulate the flow of information from distinct and independent components. Also, it is not well understand, in both theories and applications, how self propelled agents use only limited environmental information and simple rules to organize into an ordered motion. In this paper, we focus on analysis the flocking behaviour and the line-shaped pattern for collective motion invo...
Source
Source
In this paper, a generalized Motsch-Tadmor model with piecewise interaction function is investigated, which can be viewed as a generalization of the model proposed in [ 9 ]. Our analysis bases on the connectedness of the underlying graph of the system. Some sufficient conditions are presented to guarantee the system to achieve flocking. Besides, we add a stochastic disturbance to the system and consider the flocking in the sense of expectation. As results, some criterions to the flocking solutio...
Source
#1Marco Scalerandi (Polytechnic University of Turin)H-Index: 25
#2Charfeddine MechriH-Index: 8
Last. Mauro Tortello (Polytechnic University of Turin)H-Index: 22
view all 6 authors...
Abstract Nonlinear mesoscopic materials exhibit anomalous elastic nonlinearity in which fast and slow dynamics effects are mixed up. The former is an instantaneous nonlinear phenomenon due to the explicit strain dependence of velocity and damping. Slow dynamics is a non-equilibrium effect, governed by the dependence of the linear modulus and Q-factor on the dynamic strain level: when excited at constant strain, the sample properties vary in time (over minutes or more) until they reach a new equi...
Source
#1Zhisu Liu (National University of Defense Technology)H-Index: 1
#2Xiang Li (National University of Defense Technology)H-Index: 3
Last. Xiao Wang (National University of Defense Technology)H-Index: 4
view all 4 authors...
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 information processing and reactions of individuals. By constructing two dissipative differential inequalities on position and velocity together with a continuity argument, and using the Lyapunov functional approach, we present some sufficient conditions for the existence of asymptotic flocking solutions to tw...
Source
#1Zhisu Liu (National University of Defense Technology)H-Index: 1
#2Yicheng Liu (National University of Defense Technology)H-Index: 3
Last. Xiao Wang (National University of Defense Technology)H-Index: 1
view all 3 authors...
Source
This website uses cookies.
We use cookies to improve your online experience. By continuing to use our website we assume you agree to the placement of these cookies.
To learn more, you can find in our Privacy Policy.