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Abstract
The dynamics of a delay multiparticle swarm, which contains symmetric and asymmetric pairwise influence functions, are analyzed. Two different sufficient conditions to achieve conditional flocking are obtained. One does not have a clear relationship with this delay, and the other proposes a range of processing delays that affect the emergence of a flock. It is also pointed out that if the interparticle communication function has tail dissipation, unconditional flocking can be guaranteed. Compared with the previous results, the range of the communication rate β that allows a flock to emerge has been expanded from 1/4 to 1/2.
Highlights
We further consider the flocking conditions of the delayed model proposed in [5]
(3) It is clearly pointed out that processing delay can affect the occurrence of aggregation behavior, which is manifested in the controllable range of the delay in flocking conditions
We study the emergence conditions of flocking of multiple particle swarms with processing delays, establish two sufficient conditions for conditional flocking in eorem 1 and eorem 2, and give an unconditional flocking result in eorem 3
Summary
We further consider the flocking conditions of the delayed model proposed in [5]. (1) Compared with eorem 3.1 in [5], the unconditional flocking condition ∞ψ2(r)dr ∞ is improved to ∞ψ(r)dr ∞, that is, the communication rate β is expanded from 1/4 to 1/2. We have established certain conditions for the completion of unconditional flocking in eorem 3.
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