ABSTRACT
To be able to anticipate and predict quantitatively (or even just qualitatively) the behavior of a complex, nonlinear system (CNLS) that we have introduced to for the Ÿrst time, we need to be able to model it, i.e., describe and understand the relationships between its states in terms of algebraic and differential (or difference) equations. This mathematical description allows us to model it in terms of a directed graph structure (relevant nodes and branches) and its dynamics (ODEs relating node parameters and branch transmissions), and then run computer simulations under different conditions. We need to be able to estimate the nonlinear relationships between parameters, and their initial conditions. One of the universal attributes of CNLSs is that one generally does not know all of the relevant signals (variables) and the relationships between them-we can only approximate or estimate this data. An important purpose in formulating a detailed model of a CNLS is to be able to simulate (and verify) its behavior under a variety of initial conditions and inputs in order to anticipate unintended behaviors.
