Origin of bursting through homoclinic spike adding in a neuron model.
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[1] Andrey Shilnikov,et al. How a neuron model can demonstrate co-existence of tonic spiking and bursting , 2005, Neurocomputing.
[2] Sergio Rinaldi,et al. Slow-fast limit cycles in predator-prey models , 1992 .
[3] Andrey Shilnikov,et al. Mechanism of bistability: tonic spiking and bursting in a neuron model. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.
[4] L. Chua,et al. Methods of qualitative theory in nonlinear dynamics , 1998 .
[5] Andrey Shilnikov,et al. Coexistence of Tonic Spiking Oscillations in a Leech Neuron Model , 2005, Journal of Computational Neuroscience.
[6] Andrey Shilnikov,et al. Origin of Chaos in a Two-Dimensional Map Modeling Spiking-bursting Neural Activity , 2003, Int. J. Bifurc. Chaos.
[7] Neil Fenichel. Geometric singular perturbation theory for ordinary differential equations , 1979 .
[8] Li Li,et al. Dynamics of autonomous stochastic resonance in neural period adding bifurcation scenarios , 2003 .
[9] Andrey Shilnikov,et al. Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe. , 2005, Physical review letters.
[10] Volodymyr L. Maistrenko,et al. On period-adding sequences of attracting cycles in piecewise linear maps , 1998 .
[11] B. M. Fulk. MATH , 1992 .
[12] M. A. Masino,et al. Bursting in Leech Heart Interneurons: Cell-Autonomous and Network-Based Mechanisms , 2002, The Journal of Neuroscience.
[13] Andrey Shilnikov,et al. Blue sky catastrophe in singularly perturbed systems , 2005 .
[14] Alberto Tufaile,et al. Period-adding bifurcations and chaos in a bubble column. , 2004, Chaos.
[15] E. Schwartz. Methods in Neuronal Modelling. From Synapses to Networks edited by Christof Koch and Idan Segev, MIT Press, 1989. £40.50 (xii + 524 pages) ISBN 0 262 11133 0 , 1990, Trends in Neurosciences.
[16] Nikolai F. Rulkov,et al. Subthreshold oscillations in a map-based neuron model , 2004, q-bio/0406007.
[17] Rajarshi Roy,et al. Bursting dynamics of a fiber laser with an injected signal. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.
[18] L. P. Šil'nikov,et al. ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. II , 1972 .
[19] Bo Deng,et al. Glucose-induced period-doubling cascade in the electrical activity of pancreatic β-cells , 1999, Journal of mathematical biology.
[20] Ronald L. Calabrese,et al. A model of slow plateau-like oscillations based upon the fast Na+ current in a window mode , 2001, Neurocomputing.
[21] Mark Levi,et al. A period-adding phenomenon , 1990 .
[22] Georgi S. Medvedev,et al. Reduction of a model of an excitable cell to a one-dimensional map , 2005 .
[23] V. N. Belykh,et al. Homoclinic bifurcations leading to the emergence of bursting oscillations in cell models , 2000 .
[24] E Mosekilde,et al. Bifurcation structure of a model of bursting pancreatic cells. , 2001, Bio Systems.
[25] Arun V. Holden,et al. From simple to simple bursting oscillatory behaviour via chaos in the Rose-Hindmarsh model for neuronal activity , 1992 .
[26] Teresa Ree Chay,et al. Chaos in a three-variable model of an excitable cell , 1985 .