2011, Vol. 28(3): 30501-030501 DOI: 10.1088/0256-307X/28/3/030501 | ||
Exotic Homoclinic Surface of a Saddle-Node Limit Cycle in a Leech Neuron Model | ||
YOOER Chi-Feng1,2**, WEI Fang3, XU Jian-Xue2, ZHANG Xin-Hua2 | ||
1Institute of Neuroscience, Fourth Military Medical University, Xi'an 710032 2Institute of Nonlinear Dynamics, Xi'an Jiaotong University, Xi'an 710049 3XAC Research and Development Center, Xi'an 710089 |
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收稿日期 2010-11-19 修回日期 1900-01-01 | ||
Supporting info | ||
[1] Shilnikov A and Cymbalyuk G 2005 Phys. Rev. Lett. 94 048101 [2] Shilnikov A, Calabrese R and Cymbalyuk G 2005 Phys. Rev. E 71 056214 [3] Yooer C, Xu J and Zhang X 2009 Chin. Phys. Lett. 26 080501 [4] Yooer C, Xu J and Zhang X 2009 Chin. Phys. Lett. 26 070504 [5] Turaev D V and Shilnikov L P 1995 Dokl. Math. 51 404 [6] Rinzel J 1985 Lect. Notes Math. 1151 304 [7] Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171 [8] Dellnitz M and Hohmann A 1996 Nonlinear Dynamical Systems and Chaos ed Broer H W, Van Gils S A, Hoveijn I and Takens F (Basel: Birkhauser) p 449 [9] Dellnitz M and Hohmann A 1997 Numer. Math. 75 293 [10] Dellnitz M and Junge O 2002 Handbook of Dynamical Systems II: Towards Applications ed Fiedler B, Iooss G and Kopell N (Singapore: World Scientific) p 221 [11] Hsu C S 1992 Int. J. Bifurcat. Chaos 2 727 [12] Krauskopf B, Osinga H M, Doedel E J, Henderson M E, Guckenheimer J, Vladimirsky A, Dellnitz M and Junge O 2005 Int. J. Bifurcat. Chaos 15 763 [13] Dellnitz M, Froyland G and Junge O 2001 Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems ed Fiedler B (Berlin: Springer-Verlag) p 145 [14] Doedel E J 2009 AUTO-07P: Continuation and Bifurcation Software for Ordinary Differential Equations [15] Pontryagin L S 1957 Izv. Akad. Nauk SSSR Ser. Mater. 21 605 [16] Pontryagin L S and Rodygin L V 1960 Sov. Math. Dokl. 1 237 [17] Tikhonov A N 1948 Math. Sb. 22 193 [18] Tikhonov A N 1952 Math. Sb. 31 575 [19] Fenichel N 1979 J. Diff. Eq. 31 53 |
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