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This chapter discusses the development and implementation of algorithms basedon Equation-Free/Dynamic Data Driven Applications Systems (EF/DDDAS) protocolsfor the computer-assisted study of the bifurcation structure of complexdynamical systems, such as those that arise in biology (neuronal networks, cellpopulations), multiscale systems in physics, chemistry and engineering, andsystem modeling in the social sciences. An illustrative example demonstratesthe experimental realization of a chain of granular particles (a so-calledengineered granular chain). In particular, the focus is on thedetection/stability analysis of time-periodic, spatially localized structuresreferred to as "dark breathers". Results in this chapter highlight, bothexperimentally and numerically, that the number of breathers can be controlledby varying the frequency as well as the amplitude of an "out of phase"actuation, and that a "snaking" structure in the bifurcation diagram (computedthrough standard, model-based numerical methods for dynamical systems) is alsorecovered through the EF/DDDAS methods operating on a black-box simulator. TheEF/DDDAS protocols presented here are, therefore, a step towards generalpurpose protocols for performing detailed bifurcation analyses directly onlaboratory experiments, not only on their mathematical models, but also onmeasured data.

Equation-Free Computations as DDDAS Protocols for Bifurcation Studies: A Granular Chain Example