Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Individual based and mean-field modelling of direct aggregation   We introduce two models of biological aggregation, based on randomly moving
particles with individual stochasticity depending on the perceived average
population density in their neighbourhood. In the first-order model the
location of each individual is subject to a density-dependent random walk,
while in the second-order model the density-dependent random walk acts on the
velocity variable, together with a density-dependent damping term. The main
novelty of our models is that we do not assume any explicit aggregative force
acting on the individuals; instead, aggregation is obtained exclusively by
reducing the individual stochasticity in response to higher perceived density.
We formally derive the corresponding mean-field limits, leading to nonlocal
degenerate diffusions. Then, we carry out the mathematical analysis of the
first-order model, in particular, we prove the existence of weak solutions and
show that it allows for measure-valued steady states. We also perform linear
stability analysis and identify conditions for pattern formation. Moreover, we
discuss the role of the nonlocality for well-posedness of the first-order
model. Finally, we present results of numerical simulations for both the first-
and second-order model on the individual-based and continuum levels of
description.

13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio