摘要Mechanism of period-adding cascades with chaos in a reduced leech neuron model is suggested as the bifurcation of a saddle-node limit cycle with homoclinic orbits satisfying the ``small lobe condition'', instead of the blue-sky catastrophe. In every spiking adding, the new spike emerges at the end of the spiking phase of the bursters.
Abstract:Mechanism of period-adding cascades with chaos in a reduced leech neuron model is suggested as the bifurcation of a saddle-node limit cycle with homoclinic orbits satisfying the ``small lobe condition'', instead of the blue-sky catastrophe. In every spiking adding, the new spike emerges at the end of the spiking phase of the bursters.
YOOER Chi-Feng;XU Jian-Xue;ZHANG Xin-Hua. Bifurcation of a Saddle-Node Limit Cycle with Homoclinic Orbits Satisfying the Small Lobe Condition in a Leech Neuron Model[J]. 中国物理快报, 2009, 26(8): 80501-080501.
YOOER Chi-Feng, XU Jian-Xue, ZHANG Xin-Hua. Bifurcation of a Saddle-Node Limit Cycle with Homoclinic Orbits Satisfying the Small Lobe Condition in a Leech Neuron Model. Chin. Phys. Lett., 2009, 26(8): 80501-080501.
[1] Ren W et al 1997 Int. J. Bifurcat. Chaos 71867 [2] Holden A V and Fan Y 1992 Chaos Soliton. Fract. 2 221 [3] Holden A V and Fan Y 1992 Chaos Soliton. Fract. 2 349 [4] Holden A V and Fan Y 1992 Chaos Soliton. Fract. 2 583 [5] He D R, Yen W J and Kao Y H 1985 Phys. Rev. B 31 1359 [6] Pei L, Guo F and Wu S 1986 IEEE Trans. Cir. Sys. 33 438 [7] Aroudi A E et al 2000 Int. J. Bifurcat. Chaos 10 359 [8] Straube R et al 2005 Phys. Rev. E 72 066205 [9] Elnashaie S and Ajbar A 1996 Chaos Soliton. Fract. 7 1317 [10] Elnashaie S et al 2001 Chaos Soliton. Fract. 12 1761 [11] Bonatto C and Gallas J A C 2007 Phys. Rev. E 75 055204 [12] Krauskopf B and Wieczorek S 2002 Physica D 173 97 [13] Tanaka G et al 2003 Int. J. Bifurcat. Chaos 13 3409 [14] Mosekilde E et al 2001 BioSystems 63 3 [15] Ananthakrishna G 2007 Phys. Rep. 440 113 [16] Lopez J M and Marques F 2005 Physica D 211168 [17] Neubert M G and Caswell H 2000 J. Math. Bio. 41 103 [18] Shilnikov L P 1965 Sov. Math. Dokl. 6 163 [19] Shilnikov L P 1970 Math. USSR-Sb 10 91 [20] Gavrilov N K and Shilnikov L P 1972 Math. USSR-Sb 17 467 [21] Gavrilov N K and Shilnikov L P 1973 Math. USSR-Sb 19 139 [22] Koper M T M 1995 Physica D 80 72 [23] Kuznetsov Y A 2004 Elements of Applied BifurcationTheory (New York: Springer) [24] Wiggins S 2003 Introduction to Applied NonlinearDynamical systems and Chaos (New York: Springer) [25] Cymbalyuk G S, Gaudry Q, Masino M A, and Calabrese R L2002 J. Neurosci. 22 24 [26] Hill A, Lu J, Masino M, Olsen O and Calabrese R L 2001 J. Comput. Neurosci. 10 281 [27] Cymbalyuk G S and Calabrese R L 2001 Neurocomputing 38 159 [28] Shilnikov A and Cymbalyuk G 2005 Phys. Rev. Lett. 94 048101 [29] Shilnikov A L, Calabrese R and Cymbalyuk G 2005 Phys. Rev. E 71 056214 [30] Channell P, Cymbalyuk G and Shilnikov A 2007 Phys.Rev. Lett. 98 134101 [31] Doedel E J 2009 AUTO-07P: Continuation andBifurcation Software for Ordinary Differential Equations [32] Yooer C, Xu J and Zhang X 2009 Chin. Phys. Lett. 26 070504 [33] Afraimovich V et al 1974 Sov. Math. Dokl. 151761 [34] Turaev D V et al 1987 Sov. Math. Dokl. 34 397 [35] Shilnikov L P et al 2001 Methods of QualitativeTheory in Nonlinear Dynamics (Singapore: World Scientific) p 2 [36] Terman D 1991 SIAM J. Appl. Math. 51 1418 [37] Terman D 1992 J. Nonlin. Sci. 2 135