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Emergent phenomena in an ensemble of Cucker–Smale particles under joint rooted leadership

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, South Korea

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Xiaoping Xue

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

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https://doi.org/10.1142/S0218202514500043Cited by:30 (Source: Crossref)

Abstract

We present an emergent flocking estimate in a group of interacting Cucker–Smale particles under the joint rooted leadership via the discrete-time Cucker–Smale model. It is well known that the network topology regulates the emergence of flocking, and the rooted leadership topology is the most general topology with a leader–follower structure. When the network topology satisfies a weaker rooted leadership, in which the union of neighbor graphs on infinite time-blocks is under rooted leadership, we show that the asymptotic flocking can be achieved from some class of initial configurations by generalizing the earlier result of Li and Xue using the (sp) matrix theory in Ref. 36.

Keywords:

AMSC: 92D25, 92D50, 15B48

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