Experiments, simulation and continuation are three established methods for response analysis of physical systems or models thereof, which we collectively refer to as dynamical systems (DSs).
All three approaches can be used for producing a bifurcation diagram of a specific DS. However, each approach has distinctive advantages and disadvantages.
While performing experiments is usually time- and resource intensive, it has the advantage that one investigates the actual system, which eliminates the possibility of modeling errors. Performing simulations on a computer implementation of a model of a DS, on the other hand, is considerably cheaper and it is much easier to change model parameters than in experiments.
However, simulations of sophisticated models typically require substantial computational power. Furthermore, both methods share the drawback that they can only track stable responses, a restriction that is overcome by using continuation. The idea of continuation is to employ a path-following algorithm for specific types of states of a DS, for example, equilibrium states and periodic responses, and to monitor their stability, which allows reproducing the global behaviour of a DS.
While continuation can track stable as well as unstable responses, its application is most effective on carefully derived reduced models of relatively small dimensions. A novel approach to overcome individual limitations of these methods is control based continuation, which aims at combining these methods in such a way that individual drawbacks are removed.
Contact persons: Frank Schilder and Jens Starke