On the multi-cluster flocking of the fractional Cucker–Smale model

Hyunjin Ahn; Hyunjin Ahn

doi:10.3934/mine.2024024

Mathematics in Engineering

2024, Volume 6, Issue 4: 607-647. doi: 10.3934/mine.2024024

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Research article

On the multi-cluster flocking of the fractional Cucker–Smale model

Hyunjin Ahn ^,

Department of Data Technology, Myongji University, Seoul 03674, Korea

Received: 26 January 2024 Revised: 02 July 2024 Accepted: 14 August 2024 Published: 19 August 2024

This paper demonstrates several sufficient frameworks for the multi-cluster flocking behavior of the fractional Cucker–Smale (CS) model. For this, we first employ the Caputo fractional derivative instead of the usual derivative to propose the fractional CS model with the memory effect. Then, using mathematical tools based on fractional calculus, we present suitable sufficient conditions in terms of properly separated initial data close to the multi-cluster, and well-prepared system parameters for the multi-cluster flocking of the fractional system to emerge. Finally, we offer several numerical simulations and compare them with the analytical results.
- bi-cluster flocking,
- Caputo fractional derivative,
- Cucker–Smale model,
- fractional calculus,
- multi-agent system,
- multi-cluster flocking
Citation: Hyunjin Ahn. On the multi-cluster flocking of the fractional Cucker–Smale model[J]. Mathematics in Engineering, 2024, 6(4): 607-647. doi: 10.3934/mine.2024024

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Abstract

This paper demonstrates several sufficient frameworks for the multi-cluster flocking behavior of the fractional Cucker–Smale (CS) model. For this, we first employ the Caputo fractional derivative instead of the usual derivative to propose the fractional CS model with the memory effect. Then, using mathematical tools based on fractional calculus, we present suitable sufficient conditions in terms of properly separated initial data close to the multi-cluster, and well-prepared system parameters for the multi-cluster flocking of the fractional system to emerge. Finally, we offer several numerical simulations and compare them with the analytical results.

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