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

    Authors

    G. Gambino;S. R. Choudhury

    Comments

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    Abbreviated Journal Title

    Acta Appl. Math.

    Keywords

    Hyperchaotic system; Double-Hopf bifurcation; Normal form; Adaptive; synchronization; CHAOTIC SYSTEMS; NORMAL FORMS; CHEN SYSTEM; PERTURBATION TECHNIQUE; COMPUTATION; PARAMETERS; Mathematics, Applied

    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.

    Journal Title

    Acta Applicandae Mathematicae

    Volume

    122

    Issue/Number

    1

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    269

    Last Page

    282

    WOS Identifier

    WOS:000310951700022

    ISSN

    0167-8019

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