4 Bifurcations : Control and Anti - Control

Various bifurcations exist in nonlinear dynamical systems such as complex circuits, networks, and devices. Bifurcations can be important and beneficial if they are under appropriate control. Bifurcation control and anti-control deal with modification of system bifurcative characteristics by a designed control input. Typical bifurcation control and anti-control objectives include delaying the onset of an inherent bifurcation, stabilizing a bifurcated solution or branch, changing the parameter 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 limit cycles emerging from a bifurcation mechanism, optimizing the system performance near a bifurcation point, or a combination of some of these. This article offers a brief overview of this emerging and promising field of research, putting the main subject of bifurcations control and anti-control into perspective.