Hopf bifurcation analysis and amplitude control of the modified Lorenz system

This paper is concerned with the Hopf bifurcation analysis and amplitude control of the modified Lorenz system. The Hopf bifurcation of system is investigated by utilizing the Hopf bifurcation theory and the center manifold theorem firstly. Then the direction and stability of limit cycle emerging from Hopf bifurcation are determined by the designed controller. Moreover, the amplitude of limit cycle emerging from Hopf bifurcation is controlled by a nonlinear feedback controller. Finally, numerical simulations are given to verify theoretical analysis.