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

    Authors

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

    Comments

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    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

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