Adaptive Method for the Experimental Detection of Instabilities

Motivated by numerical bifurcation detection, we present a methodology for the direct location of bifurcation points in nonlinear dynamic laboratory experiments. The procedure involves active, adaptive use of the bifurcation parameter(s) as control variable(s), coupled with the on-line identification of low-order nonlinear dynamic models from experimental time-series data. Application of the procedure to such “hard” transitions as saddle-node and subcritical Hopf bifurcations is demonstrated through simulated experiments of lumped as well as spatially distributed systems.