Hopf bifurcation of the third-order Hénon system based on an explicit criterion

In this paper, Hopf bifurcation of the third-order Hénon system is studied via a simple explicit criterion, which is derived from the Schur–Cohn Criterion. Moreover stability of Hopf bifurcation is also investigated by using the normal form method and center manifold theory for the discrete time system developed by Kuznetsov. Test results containing simulations and circuit measurement are shown to demonstrate that the criterion is correct and feasible.