Abstract:
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 q = 1 - p 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, A k = k and A k = 1, 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.
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Received 12 February 2002 Published online 9 July 2002
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Rodgers, G., Yap, Y. Growth and addition in a herding model. Eur. Phys. J. B 28, 129–132 (2002). https://doi.org/10.1140/epjb/e2002-00209-7
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DOI: https://doi.org/10.1140/epjb/e2002-00209-7