Post-Double Hopf Bifurcation Dynamics and Adaptive Synchronization of a Hyperchaotic System
Abbreviated Journal Title
Acta Appl. Math.
Hyperchaotic system; Double-Hopf bifurcation; Normal form; Adaptive; synchronization; CHAOTIC SYSTEMS; NORMAL FORMS; CHEN SYSTEM; PERTURBATION TECHNIQUE; COMPUTATION; PARAMETERS; Mathematics, Applied
In this paper a four-dimensional hyperchaotic system with only one equilibrium is considered and its double Hopf bifurcations are investigated. The general post-bifurcation and stability analysis are carried out using the normal form of the system obtained via the method of multiple scales. The dynamics of the orbits predicted through the normal form comprises possible regimes of periodic solutions, two-period tori, and three-period tori in parameter space. Moreover, we show how the hyperchaotic synchronization of this system can be realized via an adaptive control scheme. Numerical simulations are included to show the effectiveness of the designed control.
Acta Applicandae Mathematicae
"Post-Double Hopf Bifurcation Dynamics and Adaptive Synchronization of a Hyperchaotic System" (2012). Faculty Bibliography 2010s. 2651.