Hopf bifurcation analysis and control of the Newton-Leipnik system

Newton-Leipnik system is the system that has double strange attractor, and for different parameters its seven equilibrium points are all unstable. In this paper, first of all, we study the characteristics of these seven unstable equilibrium points in order to find out the Hopf bifurcation points, then design a new nonlinear controller based on the bifurcation theory of nonlinear system, and through adding the new nonlinear controller in the original system, moves the Hopf bifurcation point to a new designated position successfully.