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Abstract
We present a non-trivial lower bound for the critical coupling strength to the Cucker-Smale model with unit speed constraint and short-range communication weight from the viewpoint of a mono-cluster(global) flocking. For a long-range communication weight, the critical coupling strength is zero in the sense that the mono-cluster flocking emerges from any initial configurations for any positive coupling strengths, whereas for a short-range communication weight, a mono-cluster flocking can emerge from an initial configuration only for a sufficiently large coupling strength. Our main interest lies on the condition of non-flocking. We provide a positive lower bound for the critical coupling strength. We also present numerical simulations for the upper and lower bounds for the critical coupling strength depending on initial configurations and compare them with analytical results.
Highlights
Collective self-driven synchronized motions such as the aggregation of bacteria, flocking of birds and swarming of fish are often observed in biological complex system [19, 20, 21, 37, 44, 48, 49, 50, 51]
Our main purpose in this paper is to look for the existence of a critical coupling strength of the Cucker-Smale model with unit speed constraint
We provide the existence of the critical coupling strength κc for short-range communication weights
Summary
Collective self-driven synchronized motions such as the aggregation of bacteria, flocking of birds and swarming of fish are often observed in biological complex system [19, 20, 21, 37, 44, 48, 49, 50, 51]. They have been extensively studied in an engineering domain, because of their potential applications to unmanned aerial vehicles and client network equipments, etc.
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