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Abstract and Applied Analysis
Volume 2014, Article ID 197914, 7 pages
http://dx.doi.org/10.1155/2014/197914
Research Article

Bifurcation of Nongeneric Homoclinic Orbit Accompanied by Pitchfork Bifurcation

School of Science, China University of Geosciences (Beijing), Beijing 100083, China

Received 15 February 2014; Accepted 11 March 2014; Published 7 April 2014

Academic Editor: Yonghui Xia

Copyright © 2014 Fengjie Geng and Song Li. 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.

Linked References

  1. D. M. Zhu, “The existence of nongeneric heteroclinic orbits accompanied by saddle-node bifurcation,” Science in China, Series A, vol. 24, pp. 911–916, 1994. View at Google Scholar
  2. J. Klaus and J. Knobloch, “Bifurcation of homoclinic orbits to a saddle-center in reversible systems,” International Journal of Bifurcation and Chaos, vol. 13, no. 9, pp. 2603–2622, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. X. Liu, X. Fu, and D. Zhu, “Homoclinic bifurcation with nonhyperbolic equilibria,” Nonlinear Analysis: Theory, Methods & Applications, vol. 66, no. 12, pp. 2931–2939, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. F. Geng and Y. Xu, “Bifurcations of heteroclinic loop accompanied by pitchfork bifurcation,” Nonlinear Dynamics, vol. 70, no. 2, pp. 1645–1655, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. R. Champneys, “Codimension-one persistence beyond all orders of homoclinic orbits to singular saddle centres in reversible systems,” Nonlinearity, vol. 14, no. 1, pp. 87–112, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S.-N. Chow and X.-B. Lin, “Bifurcation of a homoclinic orbit with a saddle-node equilibrium,” Differential and Integral Equations, vol. 3, no. 3, pp. 435–466, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. X. Liu, L. Shi, and D. Zhang, “Homoclinic flip bifurcation with a nonhyperbolic equilibrium,” Nonlinear Dynamics, vol. 69, no. 1-2, pp. 655–665, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. T. Wagenknecht, “Two-heteroclinic orbits emerging in the reversible homoclinic pitchfork bifurcation,” Nonlinearity, vol. 18, no. 2, pp. 527–542, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, vol. 2 of Texts in Applied Mathematics, Springer, New York, NY, USA, 1990. View at MathSciNet