  We discuss certain basic features of the equation-free (EF) approach to
modeling and computation for complex/multiscale systems. We focus on links
between the equation-free approach and tools from systems and control theory
(design of experiments, data analysis, estimation, identification and
feedback). As our illustrative example, we choose a specific numerical task
(the detection of stability boundaries in parameter space) for stochastic
models of two simplified heterogeneous catalytic reaction mechanisms. In the
equation-free framework the stochastic simulator is treated as an experiment
(albeit a computational one). Short bursts of fine scale simulation (short
computational experiments) are designed, executed, and their results processed
and fed back to the process, in integrated protocols aimed at performing the
particular coarse-grained task (the detection of a macroscopic instability).
Two distinct approaches are presented; one is a direct translation of our
previous protocol for adaptive detection of instabilities in laboratory
experiments (Rico-Martinez et al., 2003); the second approach is motivated from
numerical bifurcation algorithms for critical point detection. A comparison of
the two approaches brings forth a key feature of equation-free computation:
computational experiments can be easily initialized at will, in contrast to
laboratory ones.
