Post-Double Hopf Bifurcation Dynamics and Adaptive Synchronization of a Hyperchaotic System

In this paper a four-dimensional hyperchaotic system with only one equilibrium isconsidered and its double Hopf bifurcations are investigated. The general post-bifurcationand stability analysis are carried out using the normal form of the system obtained viathe method of multiple scales. The dynamics of the orbits predicted through the normalform comprises possible regimes of periodic solutions, two-period tori, and three-periodtori in parameter space.Moreover, we show how the hyperchaotic synchronization of this system can be realizedvia an adaptive control scheme. Numerical simulations are included to show theeffectiveness of the designed control.