Bifurcation control: Theories, methods, and applications

Bifurcation control deals with modification of bifurcation characteristics of a parameterized nonlinear system by a designed control input. Typical bi furcation control objectives include delaying the onset of an inherent bifu rcation, stabilizing a bifurcated solution or branch, changing the paramete r value of an existing bifurcation point, modifying the shape or type of a bifurcation chain, introducing a new bifurcation at a preferable parameter value, monitoring the multiplicity, amplitude, and/or frequency of some lim it cycles emerging from bifurcation, optimizing the system performance near a bifurcation point, or a combination of some of these objectives. This ar ticle offers an overview of this emerging, challenging, stimulating, and ye t promising field of research, putting the main subject of bifurcation cont rol into perspective.