Shil'nikov Analysis of Homoclinic and Heteroclinic Orbits of the T System

    Authors

    R. A. Van Gorder;S. R. Choudhury

    Comments

    Authors: contact us about adding a copy of your work at [email protected]

    Abbreviated Journal Title

    J. Comput. Nonlinear Dyn.

    Keywords

    CHAOTIC SYSTEM; PERIODIC-ORBITS; SYNCHRONIZATION; BIFURCATION; EXISTENCE; LOOP; R-3; Engineering, Mechanical; Mechanics

    Abstract

    We study the chaotic behavior of the T system, a three dimensional autonomous nonlinear system introduced by Tigan (2005, "Analysis of a Dynamical System Derived From the Lorenz System,"Scientific Bulletin Politehnica University of Timisoara, Tomul, 50, pp. 61-72), which has potential application in secure communications. Here, we first recount the heteroclinic orbits of Tigan and Dumitru (2008, "Analysis of a 3D Chaotic System," Chaos, Solitons Fractals, 36, pp. 1315-1319), and then we analytically construct homoclinic orbits describing the observed Smale horseshoe chaos. In the parameter regimes identified by this rigorous Shil'nikov analysis, the occurrence of interesting behaviors thus predicted in the T system is verified by the use of numerical diagnostics. [DOI: 10.1115/1.4002685]

    Journal Title

    Journal of Computational and Nonlinear Dynamics

    Volume

    6

    Issue/Number

    2

    Publication Date

    1-1-2011

    Document Type

    Article

    Language

    English

    First Page

    6

    WOS Identifier

    WOS:000284964300013

    ISSN

    1555-1423

    Share

    COinS
     

    Accessibility Statement

    This item was created or digitized prior to April 24, 2027, or is a reproduction of legacy media created before that date. It is preserved in its original, unmodified state specifically for research, reference, or historical recordkeeping. In accordance with the ADA Title II Final Rule, the University Libraries provides accessible versions of archival materials upon request. To request an accommodation for this item, please submit an accessibility request form.