Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A hybrid mathematical model of collective motion under alignment and
  chemotaxis   In this paper we propose and study a hybrid discrete in continuous
mathematical model of collective motion under alignment and chemotaxis effect.
Starting from the paper by Di Costanzo et al (2015a), in which the Cucker-Smale
model (Cucker and Smale, 2007) was coupled with other cell mechanisms, to
describe the cell migration and self-organization in the zebrafish lateral line
primordium, we introduce a simplified model in which the coupling between an
alignment and chemotaxis mechanism acts on a system of interacting particles.
In particular we rely on a hybrid description in which the agents are discrete
entities, while the chemoattractant is considered as a continuous signal. The
proposed model is then studied both from an analytical and a numerical point of
view. From the analytic point of view we prove, globally in time, existence and
uniqueness of the solution. Then, the asymptotic behaviour of a linearised
version of the system is investigated. Through a suitable Lyapunov functional
we show that for $t\rightarrow +\infty$, the migrating aggregate exponentially
converges to a state in which all the particles have a same position with zero
velocity. Finally, we present a comparison between the analytical findings and
some numerical results, concerning the behaviour of the full nonlinear system.

17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn