Local sensitivity analysis for the Cucker-Smale model with random inputs

Seung-Yeal Ha; Shi Jin

doi:10.3934/krm.2018034

Article Contents

2018, Volume 11, Issue 4: 859-889. Doi: 10.3934/krm.2018034

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Local sensitivity analysis for the Cucker-Smale model with random inputs

Seung-Yeal Ha^1,2, and
Shi Jin^3,

1.
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 08826, Republic of Korea
2.
Korea Institute for Advanced Study, Hoegiro 85, Seoul, 02455, Republic of Korea
3.
Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706, USA

Received: November 30, 2017

Revised: December 31, 2017

Published: April 2018

The work of S.-Y. Ha was supported by National Research Foundation of Korea(NRF-2017R1A2B2001864), and the work of S. Jin was supported by NSF grants DMS-1522184 and DMS-1107291, and the Office of the Vice Chancellor for Research and Graduate Education at the University of Wisconsin.

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Abstract

We present pathwise flocking dynamics and local sensitivity analysis for the Cucker-Smale(C-S) model with random communications and initial data. For the deterministic communications, it is well known that the C-S model can model emergent local and global flocking dynamics depending on initial data and integrability of communication function. However, the communication mechanism between agents is not a priori clear and needs to be figured out from observed phenomena and data. Thus, uncertainty in communication is an intrinsic component in the flocking modeling of the C-S model. In this paper, we provide a class of admissible random uncertainties which allows us to perform the local sensitivity analysis for flocking and establish stability to the random C-S model with uncertain communication.

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Mathematics Subject Classification: Primary: 15B48; Secondary: 92D25.

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