Hopf bifurcation analysis of a new modified hyperchaotic Lü system

The Hopf bifurcation of a new modified hyperchaotic Lü system with only one equilibrium is investigated in this paper. A detailed set of conditions are derived, which guarantee the existence of the Hopf bifurcation. Furthermore, by applying the normal form theory, the direction and type of the Hopf bifurcation, and the approximate expressions of bifurcating periodic solutions and their periods are determined. In addition, numerical simulation results supporting the theoretical analysis are given.