  This chapter discusses the development and implementation of algorithms based
on Equation-Free/Dynamic Data Driven Applications Systems (EF/DDDAS) protocols
for the computer-assisted study of the bifurcation structure of complex
dynamical systems, such as those that arise in biology (neuronal networks, cell
populations), multiscale systems in physics, chemistry and engineering, and
system modeling in the social sciences. An illustrative example demonstrates
the experimental realization of a chain of granular particles (a so-called
engineered granular chain). In particular, the focus is on the
detection/stability analysis of time-periodic, spatially localized structures
referred to as "dark breathers". Results in this chapter highlight, both
experimentally and numerically, that the number of breathers can be controlled
by varying the frequency as well as the amplitude of an "out of phase"
actuation, and that a "snaking" structure in the bifurcation diagram (computed
through standard, model-based numerical methods for dynamical systems) is also
recovered through the EF/DDDAS methods operating on a black-box simulator. The
EF/DDDAS protocols presented here are, therefore, a step towards general
purpose protocols for performing detailed bifurcation analyses directly on
laboratory experiments, not only on their mathematical models, but also on
measured data.
