Distributed delay feedback control of a new butterfly-shaped chaotic system

Delay feedback control has been proven to be one of the effective methods in the domain of continuous chaos control. In this paper, we apply distributed delay as a self-controlling feedback to implement continuous control of a new butterfly-shaped chaotic system. We investigate the local stability and the existence of Hopf bifurcation of this system. The direction and stability of the bifurcating periodic solutions are obtained by using the normal form theory and center manifold theorem. Stability and Hopf bifurcation properties indicate chaos vanishes as the mean time delay reaches a certain value. Finally, some numerical simulations are carried out to show the effectiveness of the theoretical analysis.