Dynamical analysis in a 4D hyperchaotic system

Inspirited by Li and Jin (Nonlinear Dyn. 67:2857?C2864 2012), this paper investigates the Hopf bifurcation of a four-dimensional hyperchaotic system with only one equilibrium. A detailed set of conditions are derived, which guarantee the existence of the Hopf bifurcation. Furthermore, the standard normal form theory is applied to determine the direction and type of the Hopf bifurcation, and the approximate expressions of bifurcating periodic solutions and their periods. In addition, numerical simulations are used to justify theoretical results.