Emerging Directions in Bifurcation Control

Abstract

In this chapter, we present some emerging directions in bifurcation control in continuous-time dynamical systems. Specifically we discuss two unconventional bifurcation control problems: anti-control of bifurcations and nonsmooth bifurcation control. Anti-control of bifurcation means introducing a new bifurcation at desired location with preferred properties by appropriate control. Nonsmooth bifurcation control via the so-called fractional power control technique, on the other hand, introduces new nonsmooth bifurcation phenomena. In particular, a new border-collision bifurcation, namely a trumpet bifurcation is induced via a fractional power control law for continuous dynamical systems. These emerging directions offer new insights, capabilities and flexibilities in the analysis and control of bifurcations in nonlinear dynamical systems.