- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 540769, 7 pages
Analysis of a New Quadratic 3D Chaotic Attractor
School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
Received 3 February 2013; Revised 10 April 2013; Accepted 28 April 2013
Academic Editor: Antonio Suárez
Copyright © 2013 Shahed Vahedi and Mohd Salmi Md Noorani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- E. Lorenz, “Deterministic nonperiodic flow,” Journal of the Atmospheric Sciences, vol. 20, no. 2, pp. 130–141, 1963.
- C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, vol. 41 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1982.
- Z. Wei, “Dynamical behaviors of a chaotic system with no equilibria,” Physics Letters A, vol. 376, no. 2, pp. 102–108, 2011.
- X. Wang and G. Chen, “A chaotic system with only one stable equilibrium,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 3, pp. 1264–1272, 2012.
- X. Wang and G. Chen, “Constructing a chaotic system with any number of equilibria,” Nonlinear Dynamics, vol. 71, pp. 429–436, 2013.
- J. Lü and G. Chen, “A new chaotic attractor coined,” International Journal of Bifurcation and Chaos, vol. 12, no. 3, pp. 659–661, 2002.
- G. Qi, G. Chen, S. Du, Z. Chen, and Z. Yuan, “Analysis of a new chaotic system,” Physica A, vol. 352, no. 2–4, pp. 295–308, 2005.
- T. Zhou, Y. Tang, and G. Chen, “Chen's attractor exists,” International Journal of Bifurcation and Chaos, vol. 14, no. 9, pp. 3167–3177, 2004.
- V. Govorukhin, “Calculation Lyapunov exponents for ODE,” 2004, http://www.mathworks.com/matlabcentral/fileexchange/4628.
- A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, “Determining Lyapunov exponents from a time series,” Physica D, vol. 16, no. 3, pp. 285–317, 1985.
- J. Kaplan and J. A. Yorke, “Chaotic behavior of multidimensional difference equations,” in Functional Differential Equations and Approximation of Fixed Points, vol. 730 of Lecture Notes in Mathematics, pp. 204–227, Springer, Berlin, Germany, 1979.
- G. A. Gottwald and I. Melbourne, “On the implementation of the 0-1 test for chaos,” SIAM Journal on Applied Dynamical Systems, vol. 8, no. 1, pp. 129–145, 2009.
- E. Zeraoulia and J. C. Sprott, 2-D Quadratic Maps and 3-D ODE Systems, vol. 73, World Scientific Publishing, Hackensack, NJ, USA, 2010.
- X. Wang, J. Li, and J. Fang, “Shil'nikov Chaos of a 3-D quadratic autonomous system with a four-wing chaotic attractor,” in Proceedings of the 30th Chinese Control Conference (CCC '11), pp. 561–565, 2011.