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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 294162, 6 pages
Constructing the Second Order Poincaré Map Based on the Hopf-Zero Unfolding Method
1School of Mechanical Engineering, Tianjin Polytechnic University, Tianjin 300072, China
2Department of Mechanics, Tianjin University, Tianjin 300072, China
Received 12 August 2013; Revised 12 September 2013; Accepted 13 September 2013
Academic Editor: Massimiliano Ferrara
Copyright © 2013 Gen Ge and Wang Wei. 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.
- M. Ferrara, C. Bianca, and L. Guerrini, “High-order moments conservation in thermostatted kinetic models,” Journal of Global Optimization, 2013.
- M. Ferrara, F. Munteanu, C. Udrişte, and D. Zugrăvescu, “Controllability of a nonholonomic macroeconomic system,” Journal of Optimization Theory and Applications, vol. 154, no. 3, pp. 1036–1054, 2012.
- M. Ferrara and C. Udrişte, “Multitime models of optimal growth,” WSEAS Transactions on Mathematics, vol. 7, no. 1, pp. 51–55, 2008.
- Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, vol. 112 of Applied Mathematical Sciences, Springer, New York, NY, USA, 2nd edition, 1998.
- P. Glendinning and C. Sparrow, “Local and global behavior near homoclinic orbits,” Journal of Statistical Physics, vol. 35, no. 5-6, pp. 645–696, 1984.
- S. V. Gonchenko, D. V. Turaev, P. Gaspard, and G. Nicolis, “Complexity in the bifurcation structure of homoclinic loops to a saddle-focus,” Nonlinearity, vol. 10, no. 2, pp. 409–423, 1997.
- T. S. Zhou, G. R. Chen, and Q. G. Yang, “Constructing a new chaotic system based on the \u Silnikov criterion,” Chaos, Solitons and Fractals, vol. 19, no. 4, pp. 985–993, 2004.
- Z. Li, G. R. Chen, and W. A. Halang, “Homoclinic and heteroclinic orbits in a modified Lorenz system,” Information Sciences, vol. 165, no. 3-4, pp. 235–245, 2004.
- Q. C. Zhang, R. L. Tian, and W. Wang, “Chaotic properties of mechanically and electrically coupled nonlinear dynamical systems,” Acta Physica Sinica, vol. 57, no. 5, pp. 2799–2804, 2008.
- Y.H. Li and S.M. Zhu, “-dimensional stable and unstable manifolds of hyperbolic singular point,” Chaos, Solitons and Fractals, vol. 29, no. 5, pp. 1155–1164, 2006.
- I. Baldomá and T. M. Seara, “Breakdown of heteroclinic orbits for some analytic unfoldings of the Hopf-zero singularity,” Journal of Nonlinear Science, vol. 16, no. 6, pp. 543–582, 2006.
- P. Yu and A. Y. T. Leung, “A perturbation method for computing the simplest normal forms of dynamical systems,” Journal of Sound and Vibration, vol. 261, no. 1, pp. 123–151, 2003.
- Q. C. Zhang and W. Wang, “Simplest normal form for the singularity of a pair of pure imaginary and a zero eigenvalue system,” Tianjin Daxue Xuebao, vol. 40, pp. 971–975, 2007.
- W. Wang and Q.C. Zhang, “Computation of the simplest normal form of a resonant double Hopf bifurcation system with the complex normal form method,” Nonlinear Dynamics, vol. 57, no. 1-2, pp. 219–229, 2009.
- A. H. Nayfeh, Method of Normal Forms, Wiley Series in Nonlinear Science, John Wiley & Sons, New York, NY, USA, 1993.
- S. Wiggins, Global Bifurcations and Chaos, vol. 73 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1988.
- F. S. Cui, C. H. Chew, J. X. Xu, and Y. L. Cai, “Bifurcation and chaos in the Duffing oscillator with a PID controller,” Nonlinear Dynamics, vol. 12, no. 3, pp. 251–262, 1997.