Post-Double Hopf Bifurcation Dynamics and Adaptive Synchronization of a Hyperchaotic System
Chaotic Dynamics
2012-11-21 v1 Dynamical Systems
Abstract
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.
Keywords
Cite
@article{arxiv.1202.5124,
title = {Post-Double Hopf Bifurcation Dynamics and Adaptive Synchronization of a Hyperchaotic System},
author = {Gaetana Gambino and Sudipto R. Choudhury},
journal= {arXiv preprint arXiv:1202.5124},
year = {2012}
}