Modeling the aggregative behavior of ants of the species Polyergus rufescens

By S. Boi, V. Capasso, D. Morale. 2000

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Stationary states of quadratic diffusion equations with long-range attraction (2011, background): “In particular, if nonlocal repulsion acts at a smaller scale with respect to nonlocal attractive forces in the large particle limit, then a nonlocal repulsion term can be replaced by a local term with nonlinear diffusion, we refer to [42, 11, 51, 52, 20, 22, 31, 49, 10, 36] for several examples.”
Blow-up in multidimensional aggregation equations with mildly singular interaction kernels (2009, background): “The simplest models based on ODEs systems [11, 17, 20, 31, 32] led to continuum descriptions [14, 13, 10, 26, 30, 35, 36] for the evolution of densities of individuals.”
Local and global well-posedness for aggregation equations and Patlak–Keller–Segel models with degenerate diffusion (2010, background): “Non-local aggregation phenomena have been studied in a wide variety of biological applications such as migration patterns in ecological systems [16, 17, 29, 51, 60] and Patlak– Keller–Segel (PKS) models of chemotaxis [28, 30, 36, 40, 53].”