On hopf bifurcation of Liu chaotic system

Since the pioneering work of Lorenz [1] and Rössler [2], it has been known that chaos can occur in systems of autonomous ordinary differential equations with as few as three variables and one or two quadratic nonlinearities. Many other chaotic systems have been discovered over the last years [3–7]. There have been extensive investigations on dynamical behaviors of these chaotic systems [8–14]. A bifurcation occurs where the solutions of a nonlinear system change their qualitative character as a parameter changes. In particular, bifurcation theory is about how the number of steady solutions of a system depends on parameters.