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.
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April 2011
Research Papers
Shil’nikov Analysis of Homoclinic and Heteroclinic Orbits of the T System Available to Purchase
Robert A. Van Gorder,
Robert A. Van Gorder
Department of Mathematics,
e-mail: [email protected]
University of Central Florida
, P.O. Box 161364, Orlando, FL 32816-1364
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S. Roy Choudhury
S. Roy Choudhury
Department of Mathematics,
e-mail: [email protected]
University of Central Florida
, P.O. Box 161364, Orlando, FL 32816-1364
Search for other works by this author on:
Robert A. Van Gorder
Department of Mathematics,
University of Central Florida
, P.O. Box 161364, Orlando, FL 32816-1364e-mail: [email protected]
S. Roy Choudhury
Department of Mathematics,
University of Central Florida
, P.O. Box 161364, Orlando, FL 32816-1364e-mail: [email protected]
J. Comput. Nonlinear Dynam. Apr 2011, 6(2): 021013 (6 pages)
Published Online: November 15, 2010
Article history
Received:
December 15, 2009
Revised:
April 26, 2010
Online:
November 15, 2010
Published:
November 15, 2010
Connected Content
A correction has been published:
On Shil’nikov Analysis of Homoclinic and Heteroclinic Orbits of the T System
Citation
Van Gorder, R. A., and Choudhury, S. R. (November 15, 2010). "Shil’nikov Analysis of Homoclinic and Heteroclinic Orbits of the T System." ASME. J. Comput. Nonlinear Dynam. April 2011; 6(2): 021013. https://doi.org/10.1115/1.4002685
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