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The geometry of mixed-mode oscillations in the Olsen model for the Peroxidase-Oxidase reaction
Homoclinic clusters and chaos associated with a folded node in a stellate cell model
1. | Department of Mathematics and Statistics, University of Sydney, Sydney, Australia |
[1] |
Jonathan E. Rubin, Justyna Signerska-Rynkowska, Jonathan D. Touboul, Alexandre Vidal. Wild oscillations in a nonlinear neuron model with resets: (Ⅱ) Mixed-mode oscillations. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 4003-4039. doi: 10.3934/dcdsb.2017205 |
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Bo Lu, Shenquan Liu, Xiaofang Jiang, Jing Wang, Xiaohui Wang. The mixed-mode oscillations in Av-Ron-Parnas-Segel model. Discrete and Continuous Dynamical Systems - S, 2017, 10 (3) : 487-504. doi: 10.3934/dcdss.2017024 |
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Theodore Vo, Richard Bertram, Martin Wechselberger. Bifurcations of canard-induced mixed mode oscillations in a pituitary Lactotroph model. Discrete and Continuous Dynamical Systems, 2012, 32 (8) : 2879-2912. doi: 10.3934/dcds.2012.32.2879 |
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Mathieu Desroches, Bernd Krauskopf, Hinke M. Osinga. The geometry of mixed-mode oscillations in the Olsen model for the Peroxidase-Oxidase reaction. Discrete and Continuous Dynamical Systems - S, 2009, 2 (4) : 807-827. doi: 10.3934/dcdss.2009.2.807 |
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Shyan-Shiou Chen, Chang-Yuan Cheng. Delay-induced mixed-mode oscillations in a 2D Hindmarsh-Rose-type model. Discrete and Continuous Dynamical Systems - B, 2016, 21 (1) : 37-53. doi: 10.3934/dcdsb.2016.21.37 |
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Tomáš Roubíček, V. Mantič, C. G. Panagiotopoulos. A quasistatic mixed-mode delamination model. Discrete and Continuous Dynamical Systems - S, 2013, 6 (2) : 591-610. doi: 10.3934/dcdss.2013.6.591 |
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José Mujica, Bernd Krauskopf, Hinke M. Osinga. A Lin's method approach for detecting all canard orbits arising from a folded node. Journal of Computational Dynamics, 2017, 4 (1&2) : 143-165. doi: 10.3934/jcd.2017005 |
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W.-J. Beyn, Y.-K Zou. Discretizations of dynamical systems with a saddle-node homoclinic orbit. Discrete and Continuous Dynamical Systems, 1996, 2 (3) : 351-365. doi: 10.3934/dcds.1996.2.351 |
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Rui Dilão, András Volford. Excitability in a model with a saddle-node homoclinic bifurcation. Discrete and Continuous Dynamical Systems - B, 2004, 4 (2) : 419-434. doi: 10.3934/dcdsb.2004.4.419 |
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Qingqing Li, Tianshou Zhou. Interlocked multi-node positive and negative feedback loops facilitate oscillations. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3139-3155. doi: 10.3934/dcdsb.2018304 |
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Ting Yang. Homoclinic orbits and chaos in the generalized Lorenz system. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 1097-1108. doi: 10.3934/dcdsb.2019210 |
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Flaviano Battelli. Saddle-node bifurcation of homoclinic orbits in singular systems. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 203-218. doi: 10.3934/dcds.2001.7.203 |
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Xiao-Biao Lin, Changrong Zhu. Saddle-node bifurcations of multiple homoclinic solutions in ODES. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1435-1460. doi: 10.3934/dcdsb.2017069 |
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Oksana Koltsova, Lev Lerman. Hamiltonian dynamics near nontransverse homoclinic orbit to saddle-focus equilibrium. Discrete and Continuous Dynamical Systems, 2009, 25 (3) : 883-913. doi: 10.3934/dcds.2009.25.883 |
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Benoît Grébert, Tiphaine Jézéquel, Laurent Thomann. Dynamics of Klein-Gordon on a compact surface near a homoclinic orbit. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 3485-3510. doi: 10.3934/dcds.2014.34.3485 |
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Shigui Ruan, Junjie Wei, Jianhong Wu. Bifurcation from a homoclinic orbit in partial functional differential equations. Discrete and Continuous Dynamical Systems, 2003, 9 (5) : 1293-1322. doi: 10.3934/dcds.2003.9.1293 |
[17] |
Jonathan E. Rubin, Justyna Signerska-Rynkowska, Jonathan D. Touboul, Alexandre Vidal. Wild oscillations in a nonlinear neuron model with resets: (Ⅰ) Bursting, spike-adding and chaos. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3967-4002. doi: 10.3934/dcdsb.2017204 |
[18] |
Xianjun Wang, Huaguang Gu, Bo Lu. Big homoclinic orbit bifurcation underlying post-inhibitory rebound spike and a novel threshold curve of a neuron. Electronic Research Archive, 2021, 29 (5) : 2987-3015. doi: 10.3934/era.2021023 |
[19] |
Peng Chen, Linfeng Mei, Xianhua Tang. Nonstationary homoclinic orbit for an infinite-dimensional fractional reaction-diffusion system. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021279 |
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Vladimir Sobolev. Canard cascades. Discrete and Continuous Dynamical Systems - B, 2013, 18 (2) : 513-521. doi: 10.3934/dcdsb.2013.18.513 |
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