Anti-control of Hopf bifurcations

Bifurcation control generally means to design a controller that is capable of modifying the bifurcation characteristics of a bifurcating nonlinear system, thereby achieving some desirable dynamical behaviors. A typical objective is to delay and/or stabilize an existing bifurcation. In this paper, we consider the problem of anti-controlling bifurcations, that is, a certain bifurcation is created at a desired location with preferred properties by appropriate control. Washout-filter-aided dynamic feedback control laws are developed for the creation of Hopf bifurcations. As Hopf bifurcations give rise to limit cycles, anti-control of Hopf bifurcations suggests a new approach for designing limit cycles with specified oscillatory behaviors into a system via feedback control when such dynamical behaviors are desirable.