| Citation: |
Maoli Chen, Xiang Li, Xiao Wang, Yicheng Liu. FLOCKING AND COLLISION AVOIDANCE OF A CUCKER-SMALE TYPE SYSTEM WITH SINGULAR WEIGHTS[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 140-152. doi: 10.11948/20190038
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FLOCKING AND COLLISION AVOIDANCE OF A CUCKER-SMALE TYPE SYSTEM WITH SINGULAR WEIGHTS
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Abstract
The dynamical behavior of a flock model with a singular communication rate and extra interaction terms is investigated in this paper. A rigorous theoretical proof of collision avoidance between any two agents is obtained which guarantees the existence of global solutions. Moreover, a sufficient condition for the existence of time-asymptotic flocking is also acquired and numerical simulations verified these results which show that a compact equilibrium configuration may emerge.-
Keywords:
- Time-asymptotic flocking /
- singular weights /
- collision avoidance
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References
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Maoli Chen, Xiang Li, Xiao Wang, Yicheng Liu. FLOCKING AND COLLISION AVOIDANCE OF A CUCKER-SMALE TYPE SYSTEM WITH SINGULAR WEIGHTS[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 140-152. doi: 10.11948/20190038
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Figure 1. Trajectories of the velocities of the 5 agents with
$ \alpha = 0.2,\ R = 5 $ . - Figure 2. The equilibrium configurations have the following two forms: (a): the five particles at the apex of the regular pentagon; (b): all agents are distributed at the four vertices of a square and its center.
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Figure 3. Trajectories of the velocities of the 10 particles with
$ \alpha = 0.1,\ R = 5 $ . - Figure 4. The pictures show the equilibrium configurations may have two cases: (a): nine agents at the vertices of the regular hexagon and one particle at its center; (b): eight agents are distributed at the vertices of the regular octagon to form an outer ring; the remaining ones are stably and evenly located inside the outer ring eventually.