| Preface |
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PART I: BURSTING AT THE SINGLE CELL LEVEL |
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The Development of the Hindmarsh-Rose Model for Bursting |
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3 | (16) |
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3 | (1) |
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4 | (1) |
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5 | (3) |
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8 | (2) |
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Subthreshold Oscillations |
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10 | (5) |
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15 | (4) |
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Negative Calcium Feedback: The Road from Chay-Keizer |
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19 | (30) |
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19 | (1) |
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20 | (4) |
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24 | (8) |
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32 | (2) |
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The Return of K(Ca): Help from the Endoplasmic Reticulum |
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34 | (7) |
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Further Modifications to the Model |
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41 | (2) |
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43 | (6) |
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Autoregulation of Bursting of AVP Neurons of the Rat Hypothalamus |
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49 | (40) |
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49 | (3) |
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Electrical Properties of AVP Cells |
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52 | (3) |
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55 | (3) |
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58 | (1) |
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58 | (4) |
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62 | (1) |
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62 | (4) |
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66 | (5) |
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The Dynamics of Dynorphin |
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71 | (2) |
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73 | (8) |
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73 | (1) |
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73 | (8) |
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81 | (8) |
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81 | (1) |
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Alternative mechanisms for the plateau potential |
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81 | (1) |
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82 | (7) |
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Bifurcations in the Fast Dynamics of Neurons: Implications for Bursting |
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89 | (34) |
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90 | (1) |
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A Two Dimensional Model of Spiking Sodium Currents |
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91 | (13) |
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Fast-Slow Analysis of Bursting |
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104 | (11) |
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106 | (2) |
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108 | (2) |
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110 | (2) |
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Plateau oscillations in leech heart interneurons |
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112 | (1) |
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Neurons of the pre-Botzinger complex |
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113 | (2) |
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115 | (8) |
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Bursting in 2-Compartment Neurons: A Case Study of the Pinsky-Rinzel Model |
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123 | (22) |
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123 | (2) |
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125 | (4) |
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Equations and qualitative description of the complex burst |
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125 | (4) |
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Dynamics of the Pinsky-Rinzel Model |
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129 | (8) |
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129 | (4) |
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Somatic-dendritic ping-pong |
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133 | (4) |
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Morris-Lecar Two-Compartment Models |
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137 | (3) |
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140 | (5) |
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Ghostbursting: The Role of Active Dendrites in Electrosensory Processing |
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145 | (30) |
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145 | (1) |
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146 | (5) |
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151 | (3) |
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154 | (3) |
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Extensions and Other Work |
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157 | (6) |
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158 | (1) |
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159 | (1) |
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160 | (1) |
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Differential modulation of burst discharge |
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161 | (2) |
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Parallel Processing with Bursts and Isolated Spikes |
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163 | (6) |
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Ghostbusting the ghostburster |
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163 | (3) |
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166 | (3) |
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169 | (6) |
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PART II: BURSTING AT THE NETWORK LEVEL |
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Analysis of Circuits Containing Bursting Neurons Using Phase Resetting Curves |
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175 | (26) |
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175 | (3) |
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Stability Analysis for Two Coupled Oscillators |
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178 | (3) |
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Analysis of a Circuit of Two Model Neurons |
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181 | (2) |
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Stability Analysis for a Three Neuron Ring Circuit |
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183 | (3) |
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Analysis of a Circuit of Three Model Neurons |
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186 | (3) |
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Analysis of a Two Neuron Hybrid Circuit |
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189 | (2) |
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Effect of Changing Burst Durations in the Two Neuron Circuit |
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191 | (2) |
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Phenomenology of Resetting in a Biological Bursting, Neuron |
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193 | (2) |
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195 | (6) |
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Bursting in Coupled Cell Systems |
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201 | (22) |
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201 | (2) |
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Unfolding Theory and Bursting in Fast-Slow Systems |
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203 | (2) |
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Bursting in Two Coupled Cells |
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205 | (2) |
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Z2-Equivariant Bifurcations |
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207 | (2) |
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209 | (2) |
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Hopf/Hopf Mode Interactions |
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211 | (2) |
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Takens-Bogdanov Bifurcation with Z2 Symmetry |
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213 | (6) |
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219 | (4) |
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Modulatory Effects of Coupling on Bursting Maps |
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223 | (20) |
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223 | (2) |
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Examples of Bursting Maps |
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225 | (5) |
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225 | (1) |
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226 | (4) |
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230 | (4) |
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Effects of coupling on one-dimensional maps |
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230 | (2) |
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Effects of coupling on two-dimensional maps |
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232 | (2) |
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Rulkov's First Bursting Map: Explaining the Effect of Coupling |
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234 | (4) |
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238 | (5) |
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Beyond Synchronization: Modulatory and Emergent Effects of Coupling in Square-Wave Bursting |
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243 | (30) |
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243 | (2) |
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245 | (2) |
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Effect of Coupling: Identical Cells |
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247 | (7) |
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Effects of coupling on spike patterns |
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249 | (2) |
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Effects of coupling on burst period |
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251 | (3) |
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254 | (4) |
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255 | (1) |
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Stability of the in-phase and anti-phase steady states |
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256 | (1) |
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Non-identical cells: Δ ≠ 1 |
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257 | (1) |
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Enhancement of the Period Extension with Heterogeneity |
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258 | (3) |
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261 | (4) |
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265 | (2) |
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267 | (6) |
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Limitations and extensions |
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267 | (2) |
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Comparison to other emergent oscillations |
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269 | (4) |
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Bursting in Excitatory Neural Networks |
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273 | (30) |
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274 | (1) |
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Spontaneous Activity in the Developing Spinal Cord |
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274 | (3) |
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Model of the Spontaneous Activity in the Embryonic Chick Spinal Cord |
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277 | (3) |
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Properties and Applications of the Model |
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280 | (12) |
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Bistability of the excitatory network with fixed synaptic efficacy |
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280 | (3) |
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Episodic and rhythmic behavior due to activity-dependent depression of network excitability |
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283 | (4) |
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Relationship between episode duration and inter-episode interval |
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287 | (2) |
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Recovery of the activity after blockade of excitatory connections |
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289 | (3) |
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Analogy between Network and Cellular Bursting |
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292 | (2) |
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294 | (9) |
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Bursting activity in neural networks |
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295 | (1) |
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Network vs cellular bursting |
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296 | (7) |
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Oscillatory Bursting Mechanisms in Respiratory Pacemaker Neurons and Networks |
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303 | (44) |
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304 | (2) |
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Single Cell Dynamics: Evidence, Motivation, and Models |
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306 | (6) |
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Coupling Effects in Two Cells: A Pathway to Larger Populations |
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312 | (2) |
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The Big Bang: Populations of Excitatory Pacemakers |
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314 | (4) |
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Synchronized bursting in a heterogeneous population |
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314 | (2) |
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Dynamic range of network oscillations |
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316 | (1) |
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Emergent rhythms: Pacemakers vs. group pacemakers |
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317 | (1) |
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Dynamic Range of Bursting Activity |
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318 | (11) |
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Fast/slow analysis of a single cell |
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318 | (5) |
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The transition from bursting to spiking in coupled cells with h1 = h2 |
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323 | (4) |
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The transition from bursting to tonic spiking in the full model for two coupled cells |
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327 | (2) |
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329 | (9) |
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Motivation and introduction to modeling approach |
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329 | (1) |
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The role of fast threshold modulation |
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330 | (3) |
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Analysis of a synchronized bursting in a heterogeneous population |
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333 | (5) |
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Contemporary Issues and Unresolved Problems |
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338 | (9) |
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Single neuron properties and models |
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338 | (2) |
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Analysis of coupled cells and networks |
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340 | (7) |
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Geometric Analysis of Bursting Networks |
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347 | (38) |
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348 | (1) |
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Existence, Uniqueness and Stability of Square-Wave Bursters |
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349 | (9) |
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Assumptions on the geometric model |
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350 | (2) |
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352 | (1) |
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352 | (1) |
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When do trajectories jump down? |
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353 | (2) |
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Return map and outline of the proof |
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355 | (3) |
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Propagating Activity Patterns |
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358 | (9) |
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358 | (3) |
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361 | (1) |
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Singular construction of smooth waves |
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362 | (2) |
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Estimating the wave speed |
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364 | (3) |
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Transitions between Irregular and Clustered Activity |
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367 | (18) |
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367 | (2) |
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Two distinct activity patterns |
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369 | (1) |
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Geometric analysis of irregular activity |
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370 | (5) |
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Geometric analysis of clustered activity |
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375 | (4) |
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Transitions and dependence on parameters |
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379 | (6) |
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Elliptic Bursters, Depolarization Block, and Waves |
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385 | (12) |
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385 | (2) |
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387 | (1) |
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388 | (6) |
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388 | (2) |
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Breaking up is easy to do |
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390 | (2) |
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392 | (1) |
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393 | (1) |
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394 | (3) |
| Index |
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