Towards a mathematical theory of behavioral swarms
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 125.

This paper presents a unified mathematical theory of swarms where the dynamics of social behaviors interacts with the mechanical dynamics of self-propelled particles. The term behavioral swarms is introduced to characterize the specific object of the theory which is subsequently followed by applications. As concrete examples for our unified approach, we show that several Cucker-Smale type models with internal variables fall down to our framework. The second part of the paper shows how the modeling can be developed, beyond the Cucker-Smale approach. This will be illustrated with the aid of numerical simulations in swarms whose movement strategy is sensitive to individual social behaviors. Finally, the presentation looks ahead to research perspectives.

DOI : 10.1051/cocv/2020071
Classification : 82D99, 91D10
Mots-clés : Collective dynamics, Cucker-Smale flocking, learning, living systems, self-organization, swarming 
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     author = {Bellomo, Nicola and Ha, Seung-Yeal and Outada, Nisrine},
     editor = {Buttazzo, G. and Casas, E. and de Teresa, L. and Glowinsk, R. and Leugering, G. and Tr\'elat, E. and Zhang, X.},
     title = {Towards a mathematical theory of behavioral swarms},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {26},
     year = {2020},
     doi = {10.1051/cocv/2020071},
     mrnumber = {4188831},
     zbl = {1459.82166},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv/2020071/}
}
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Bellomo, Nicola; Ha, Seung-Yeal; Outada, Nisrine. Towards a mathematical theory of behavioral swarms. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 125. doi : 10.1051/cocv/2020071. http://www.numdam.org/articles/10.1051/cocv/2020071/

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