A Multi-Agent System is a distributed system where the agents or nodes
perform complex functions that cannot be written down in analytic form.
Multi-Agent Systems are highly connected, and the information they contain is
mostly stored in the connections. When agents update their state, they take
into account the state of the other agents, and they have access to those
states via the connections. There is also external, user-generated input into
the Multi-Agent System. As so much information is stored in the connections,
agents are often memory-less. This memory-less property, together with the
randomness of the external input, has allowed us to model Multi-Agent Systems
using Markov chains. In this paper, we look at Multi-Agent Systems that evolve,
i.e. the number of agents varies according to the fitness of the individual
agents. We extend our Markov chain model, and define stability. This is the
start of a methodology to control Multi-Agent Systems. We then build upon this
to construct an entropy-based definition for the degree of instability (entropy
of the limit probabilities), which we used to perform a stability analysis. We
then investigated the stability of evolving agent populations through
simulation, and show that the results are consistent with the original
definition of stability in non-evolving Multi-Agent Systems, proposed by Chli
and De Wilde. This paper forms the theoretical basis for the construction of
Digital Business Ecosystems, and applications have been reported elsewhere.Comment: 9 pages, 5 figures, journa