Control algorithm for creation of Hopf bifurcations in continuous-time systems of arbitrary dimension

Creation of Hopf bifurcations via appropriate controls is viewed as one way of designing oscillatory behaviors into a dynamical system. A general control algorithm is proposed for creation of Hopf bifurcation at a desired parameter point in nonlinear systems of arbitrary dimension. The linear gains that control the two critical bifurcation conditions are derived according to the suitable criteria without using eigenvalues, and the nonlinear gains that control the stability of the created limit circle are analytically derived by utilizing the center manifold theory and normal form reduction. The control law allows us to develop a desirable oscillatory behavior in high-dimensional systems. Applications are illustrated for an eight-dimensional chaotic system.