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Bifurcations of a nongeneric heteroclinic loop with nonhyperbolic equilibria
1. | College of Mathematics and Science, China University of Geosciences(Beijing), Beijing, 100083, China, China |
2. | Department of Mathematics, East China Normal University, Shanghai, 200241 |
3. | Department of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, 130024, China |
References:
[1] |
S. N. Chow, B. Deng and J. M. Friedman, Theory and applicationsof a nongeneric heteroclinic loop bifurcation, SIAM J. Appl. Math., 59 (1999), 1303-1321. |
[2] |
A. R. Champneys, Codimension-one persistence beyond allorders of homoclinic orbits to singular saddle centres in reversible systems, Nonlinearity, 14 (2001), 87-112. |
[3] |
F. J. Geng, D. Liu and D. M. Zhu, Bifurcations of generic heteroclinic loop accompanied by transcritical bifurcation, International J. Bifurcation and Chaos, 4 (2008), 1069-1083. |
[4] |
X. B. Liu, X. L. Fu and D. M. Zhu, Homoclinic Bifurcation with non hyperbolic equilibria, Nonlinear Analysis, 66 (2007), 2931-2939.
doi: 10.1016/j.na.2006.04.014. |
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X. B. Liu and D. M. Zhu, Homoclinic snaking near a heteroclinic cycles inreversible systems, Appl. Math. J. Chinese Univ. Ser. A (in Chinese), 19 (2004), 401-408. |
[6] |
J. D. M. Rademacher, Homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit, J. Differential Equations, 218 (2005), 390-443.
doi: 10.1016/j.jde.2005.03.016. |
[7] |
J. H. Sun and D. J. Luo, Local and global bifurcations with nonhyperbolic equilibria, Science in China, Series A, 37 (1994), 523-534. |
[8] |
S. Wiggins, "Introduction to Applied Nonlinear Dynamical Systems and Chaos," Springer-Verlag, New York, 1990. |
[9] |
D. M. Zhu and Z. H. Xia, Bifurcations of Morse-Smale dynamical systems, Science in China, Series A, 41 (1998), 837-848. |
show all references
References:
[1] |
S. N. Chow, B. Deng and J. M. Friedman, Theory and applicationsof a nongeneric heteroclinic loop bifurcation, SIAM J. Appl. Math., 59 (1999), 1303-1321. |
[2] |
A. R. Champneys, Codimension-one persistence beyond allorders of homoclinic orbits to singular saddle centres in reversible systems, Nonlinearity, 14 (2001), 87-112. |
[3] |
F. J. Geng, D. Liu and D. M. Zhu, Bifurcations of generic heteroclinic loop accompanied by transcritical bifurcation, International J. Bifurcation and Chaos, 4 (2008), 1069-1083. |
[4] |
X. B. Liu, X. L. Fu and D. M. Zhu, Homoclinic Bifurcation with non hyperbolic equilibria, Nonlinear Analysis, 66 (2007), 2931-2939.
doi: 10.1016/j.na.2006.04.014. |
[5] |
X. B. Liu and D. M. Zhu, Homoclinic snaking near a heteroclinic cycles inreversible systems, Appl. Math. J. Chinese Univ. Ser. A (in Chinese), 19 (2004), 401-408. |
[6] |
J. D. M. Rademacher, Homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit, J. Differential Equations, 218 (2005), 390-443.
doi: 10.1016/j.jde.2005.03.016. |
[7] |
J. H. Sun and D. J. Luo, Local and global bifurcations with nonhyperbolic equilibria, Science in China, Series A, 37 (1994), 523-534. |
[8] |
S. Wiggins, "Introduction to Applied Nonlinear Dynamical Systems and Chaos," Springer-Verlag, New York, 1990. |
[9] |
D. M. Zhu and Z. H. Xia, Bifurcations of Morse-Smale dynamical systems, Science in China, Series A, 41 (1998), 837-848. |
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