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Hopf bifurcation of the third-order Hénon system based on an explicit criterion. (English) Zbl 1158.93364

Summary: 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.

MSC:

93C55 Discrete-time control/observation systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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