Controlling the multiplicity of limit cycles

Bifurcation control refers to the task of modifying certain bifurcative dynamical behavior of a nonlinear system that is desirable for an intended application, by means of designing an appropriate controller. In this paper, the problem of controlling the multiplicity of periodic solutions of a nonlinear systems is addressed. The approach utilizes the system curvature coefficients (or stability indexes) obtained via higher-order harmonic balance approximations. A typical example (Sibirskii´s example, 1965) of a planar cubic system is presented for illustration