Bifurcation analysis and chaos control in Shimizu–Morioka chaotic system with delayed feedback

We investigate the local Hopf bifurcation in Shimizu–Morioka chaotic system with delayed feedback control. We choose the delay as the parameter, and the existence of local Hopf bifurcations are verified. By using the normal form theory and the center manifold theorem, we obtain the explicit formulae for determining the stability and direction of bifurcated periodic solutions. Numerical simulations indicate that delayed feedback control plays an effective role in control of chaos.