Journal
ARBOR-CIENCIA PENSAMIENTO Y CULTURA
Volume 186, Issue 746, Pages 1035-1049Publisher
CONSEJO SUPERIOR INVESTIGACIONES CIENTIFICAS-CSIC
DOI: 10.3989/arbor.2010.746n1252
Keywords
Swarming; individual-based models; pattern formation; mean-field limits; kinetic theory
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Funding
- ICREA Funding Source: Custom
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In this short note we review some of the individual based models of the collective motion of agents, called swarming. These models based on ODEs (ordinary differential equations) exhibit a complex rich asymptotic behavior in terms of patterns, that we show numerically. Moreover, we comment on how these particle models are connected to partial differential equations to describe the evolution of densities of individuals in a continuum manner. The mathematical questions behind the stability issues of these PDE (partial differential equations) models are questions of actual interest in mathematical biology research.
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