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An Introduction to Modeling Neuronal Dynamics

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Cover of 'An Introduction to Modeling Neuronal Dynamics'

Table of Contents

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    Book Overview
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    Chapter 1 Vocabulary and Notation
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    Chapter 2 The Nernst Equilibrium
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    Chapter 3 The Classical Hodgkin-Huxley ODEs
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    Chapter 4 Numerical Solution of the Hodgkin-Huxley ODEs
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    Chapter 5 Three Simple Models of Neurons in Rodent Brains
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    Chapter 6 The Classical Hodgkin-Huxley PDEs
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    Chapter 7 Linear Integrate-and-Fire (LIF) Neurons
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    Chapter 8 Quadratic Integrate-and-Fire (QIF) and Theta Neurons
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    Chapter 9 Spike Frequency Adaptation
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    Chapter 10 The Slow-Fast Phase Plane
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    Chapter 11 Saddle-Node Collisions
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    Chapter 12 Model Neurons of Bifurcation Type 1
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    Chapter 13 Hopf Bifurcations
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    Chapter 14 Model Neurons of Bifurcation Type 2
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    Chapter 15 Canard Explosions
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    Chapter 16 Model Neurons of Bifurcation Type 3
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    Chapter 17 Frequency-Current Curves
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    Chapter 18 Bistability Resulting from Rebound Firing
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    Chapter 19 Bursting
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    Chapter 20 Chemical Synapses
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    Chapter 21 Gap Junctions
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    Chapter 22 A Wilson-Cowan Model of an Oscillatory E-I Network
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    Chapter 23 Entrainment by Excitatory Input Pulses
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    Chapter 24 Synchronization by Fast Recurrent Excitation
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    Chapter 25 Phase Response Curves (PRCs)
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    Chapter 26 Synchronization of Two Pulse-Coupled Oscillators
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    Chapter 27 Oscillators Coupled by Delayed Pulses
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    Chapter 28 Weakly Coupled Oscillators
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    Chapter 29 Approximate Synchronization by a Single Inhibitory Pulse
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    Chapter 30 The PING Model of Gamma Rhythms
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    Chapter 31 ING Rhythms
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    Chapter 32 Weak PING Rhythms
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    Chapter 33 Beta Rhythms
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    Chapter 34 Nested Gamma-Theta Rhythms
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    Chapter 35 Rhythmic vs. Tonic Inhibition
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    Chapter 36 Rhythmic vs. Tonic Excitation
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    Chapter 37 Gamma Rhythms and Cell Assemblies
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    Chapter 38 Gamma Rhythms and Communication
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    Chapter 39 Short-Term Depression and Facilitation
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    Chapter 40 Spike Timing-Dependent Plasticity (STDP)
Attention for Chapter 2: The Nernst Equilibrium
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Chapter title
The Nernst Equilibrium
Chapter number 2
Book title
An Introduction to Modeling Neuronal Dynamics
Published by
Springer, Cham, January 2017
DOI 10.1007/978-3-319-51171-9_2
Book ISBNs
978-3-31-951170-2, 978-3-31-951171-9
Authors

Christoph Börgers