  We discuss a specific model, which we refer to as RandLOE, of a large
multi-agent network whose dynamic is prescribed via a combination of
deterministic local laws and random exogenous factors. The RandLOE approach
lies outside the framework of Stochastic Differential Equations, but lends
itself to analytic examination as well as to stable simulation even for
relatively large networks. RandLOE is based on the logistic operator equation
(LOE), which is a multidimensional dynamical system extending the classical
logistic equation via an operator-algebraic interaction term. The network is
defined by interpreting the LOE variable as an adjacency matrix of a complete
graph. Depending on the choice of parameters, it can display a number of
essentially distinct dynamical characteristics: e.g. cycles of expansion and
contraction.
