Multi-Cluster Flocking Behavior Analysis for a Delayed Cucker-Smale Model with Short-Range Communication Weight
Tóm tắt
This paper analyzes the multi-cluster flocking behavior of a Cucker-Smale model involving delays and a short-range communication weight. In each sub-flocking group, the velocity between agents is alignment and the position locates at a limited domain; but in different sub-flocking groups, the position between agents is unbounded. By constructing dissipative differential inequalities of sub-ensembles together with Lyapunov functional methods, the authors provide the sufficient condition for the multi-cluster flocking emerging. The sufficient condition includes the estimation of the range of coupling strength and the upper bound of time delay. As a result, the authors show that the coupling strength among agents and initial threshold value determine the multi-cluster flocking behavior of the delayed Cucker-Smale model.
Tài liệu tham khảo
Reynolds C, Flocks, herds and schools: A distributed behavioral model, Computer Graphics, 1987, 21(4): 25–34.
Vicsek T, Czirok A, Ben-Jacob E, et al., Novel type of phase transition in a system of self-driven particles, Physical Review Letters, 2006, 75(6): 1226–1229.
Cucker F and Smale S, Emergent behavior in flocks, IEEE Transactions on Automatic Control, 2007, 52(5): 852–862.
Cucker F and Smale S, On the mathematics of emergence, Japanese Journal of Mathematics, 2007, 2(1): 197–227.
Ha S Y and Liu J G, A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Communications in Mathematical Sciences, 2009, 7(2): 297–325.
Shen J, Cucker-Smale flocking under hierarchical leadership, SIAM Journal on Applied Mathematics, 2007, 68(3): 694–719.
Li Z C and Xue X P, Cucker-Smale flocking under rooted leadership with fixed and switching topologies, SIAM Journal on Applied Mathematics, 2010, 70(7): 3156–3174.
Dong J G and Qiu L, Flocking of the Cucker-Smale model on general digraphs, IEEE Transactions on Automatic Control, 2017, 62(10): 5234–5239.
Ru L N and Xue X P, Multi-cluster flocking behavior of the hierarchical Cucker-Smale model, Journal of the Franklin Institute, 2017, 354(5): 2371–2392.
Cho J, Ha S Y, and Huang F, Emergence of bi-cluster flocking for agent-based models with unit speed constraint, Analysis & Applications, 2016, 14(1): 39–73.
Cho J, Ha S Y, and Huang F, Emergence of bi-cluster flocking for the Cucker-Smale model, Mathematical Models and Methods in Applied Sciences, 2016, 26(6): 1191–1218.
Ha S Y, Ko D, and Zhang Y, Critical coupling strength of the Cucker-Smale model for flocking, Mathematical Models and Methods in Applied Sciences, 2017, 27(6): 1051–1087.
Liu Y C and Wu J H, Flocking and asymptotic velocity of the Cucker-Smale model with processing delay, Journal of Mathematical Analysis & Applications, 2014, 415(1): 53–61.
Young-Pil C and Jan H, Cucker-Smale model with normalized communication weights and time delay, Kinetic & Related Models, 2016, 10(4): 1011–1033.
Cristina P and Irene R V, Flocking estimates for the Cucker-Smale model with time lag and hierarchical leadership, Journal of Mathematical Analysis & Applications, 2017, 464(2): 1313–1332.
Erban R, HasKovec J, and Sun Y, A Cucker-Smale model with noise and delay, SIAM Journal on Applied Mathematics, 2015, 76(4): 1535–1557.
Young-Pil C and Li Z C, Emergent behavior of Cucker-Smale flocking particles with time delays, Applied Mathematics Letters, 2018, 86: 49–56.