https://doi.org/10.1140/epjb/e2002-00209-7
Growth and addition in a herding model
Department of Mathematical Sciences, Brunel University,
Uxbridge, Middlesex UB8 3PH, UK
Corresponding author: a g.j.rodgers@brunel.ac.uk
Received:
12
February
2002
Published online:
9
July
2002
A model of herding is introduced
which is exceptionally simple, incorporating only two
phenomena, growth and addition.
At each time step either (i) with probability p
the system
grows through the introduction of a new agent or (ii)
with probability 
a free agent already
in the system is added at random to a group of size k with
rate Ak.
Two versions of the model, 
and 
, are solved
and in both versions we find two different types of behaviour.
When p>1/2 all the moments of the distribution of group sizes
are linear in time for large time and the group distribution is
power-law. When p<1/2 the system runs out of
free agents in a finite time.
PACS: 02.50.cw – Probability theory / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 89.75Hc. – Networks and genealogical trees
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002
