  Stability is perhaps one of the most desirable features of any engineered
system, given the importance of being able to predict its response to various
environmental conditions prior to actual deployment. Engineered systems are
becoming ever more complex, approaching the same levels of biological
ecosystems, and so their stability becomes ever more important, but taking on
more and more differential dynamics can make stability an ever more elusive
property. The Chli-DeWilde definition of stability views a Multi-Agent System
as a discrete time Markov chain with potentially unknown transition
probabilities. With a Multi-Agent System being considered stable when its
state, a stochastic process, has converged to an equilibrium distribution,
because stability of a system can be understood intuitively as exhibiting
bounded behaviour. We investigate an extension to include Multi-Agent Systems
with evolutionary dynamics, focusing on the evolving agent populations of our
Digital Ecosystem. We then built upon this to construct an entropy-based
definition for the degree of instability (entropy of the limit probabilities),
which was later used to perform a stability analysis. The Digital Ecosystem is
considered to investigate the stability of an evolving agent population through
simulations, for which the results were consistent with the original
Chli-DeWilde definition.
