Emergencies as a manifestation of the effect of bifurcation memory in controlled unstable systems

Unusual behavior of dynamic systems with a control parameter is analyzed. Bifurcation induced qualitative changes in phase portraits of such systems are quite routine and ensure efficient operation. This class of systems includes ships with high maneuvering capabilities, aircraft and controlled underwater vehicles designed to be unstable in steady-state motion that are interesting in terms of applications. Bifurcations may generate tracks of bifurcation memory that are "indicators" of regions of reduced controllability referred to as phase spots. The transition process in the phase spot is estimated qualitatively as a universal dependence of the index of loss of controllability on the control parameter. The proposed approach has allowed us to predict and investigate emergency manifestations of the bifurcation memory effect occurring during routine maneuvering.