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.
Skip Nav Destination
e-mail: rav@knights.ucf.edu
e-mail: choudhur@cs.ucf.edu
Article navigation
April 2011
Research Papers
Shil’nikov Analysis of Homoclinic and Heteroclinic Orbits of the T System
Robert A. Van Gorder,
Robert A. Van Gorder
Department of Mathematics,
e-mail: rav@knights.ucf.edu
University of Central Florida
, P.O. Box 161364, Orlando, FL 32816-1364
Search for other works by this author on:
S. Roy Choudhury
S. Roy Choudhury
Department of Mathematics,
e-mail: choudhur@cs.ucf.edu
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: rav@knights.ucf.edu
S. Roy Choudhury
Department of Mathematics,
University of Central Florida
, P.O. Box 161364, Orlando, FL 32816-1364e-mail: choudhur@cs.ucf.edu
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
Download citation file:
Get Email Alerts
Investigation of Nonlinear Dynamic Behaviors of Vertical Rotor System Supported by Aerostatic Bearings
J. Comput. Nonlinear Dynam (January 2025)
Electric Circuit Analogs of First-Order Dual-Phase-Lag Diffusion
J. Comput. Nonlinear Dynam
Related Articles
Measures of Order in Dynamic Systems
J. Comput. Nonlinear Dynam (July,2008)
Introduction
J. Comput. Nonlinear Dynam (October,2006)
Analytical Predication of Complex Motion of a Ball in a Periodically Shaken Horizontal Impact Pair
J. Comput. Nonlinear Dynam (April,2012)
Shilnikov Chaos and Dynamics of a Self-Sustained Electromechanical Transducer
J. Vib. Acoust (April,2001)
Related Chapters
A Study on Aging Characteristics of the XLPE Cable Based on Chaos-Fractal Theory
International Conference on Mechanical and Electrical Technology, 3rd, (ICMET-China 2011), Volumes 1–3
Ultra High-Speed Microbridge Chaos Domain
Intelligent Engineering Systems Through Artificial Neural Networks, Volume 17
The Applications of the Cloud Theory in the Spatial DMKD
International Conference on Electronics, Information and Communication Engineering (EICE 2012)