An Introduction to Modeling Neuronal Dynamics
This book is intended as a text for a one-semester course on Mathematical and Computational Neuroscience for upper-level undergraduate and beginning graduate students of mathematics, the natural sciences, engineering, or computer science. An undergraduate introduction to differential equations is mo...
| Κύριος συγγραφέας: | |
|---|---|
| Συγγραφή απο Οργανισμό/Αρχή: | |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
Cham :
Springer International Publishing : Imprint: Springer,
2017.
|
| Σειρά: | Texts in Applied Mathematics,
66 |
| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- Vocabulary and Notation
- Modeling a Single Neuron
- The Nernst Equilibrium
- The Classical Hodgkin-Huxley ODEs
- Numerical Solution of the Hodgkin-Huxley ODEs
- Three Simple Models of Neurons in Rodent Brains
- The Classical Hodgkin-Huxley PDEs
- Linear Integrate-and-fire (LIF) Neurons
- Quadratic Integrate-and-fire (QIF) and Theta Neurons
- Spike Frequency Adaptation
- Dynamics of Single Neuron Models
- The Slow-fast Phase Plane
- Saddle-node Collisions
- Model Neurons of Bifurcation Type 1
- Hopf Bifurcations
- Model Neurons of Bifurcation Type 2
- Canard Explosions
- Model Neurons of Bifurcation Type 3
- Frequency-current Curves
- Bistability Resulting from Rebound Firing
- Bursting
- Modeling Nuronal Communication
- Chemical Synapses
- Gap Junctions
- A Wilson-Cowan Model of an Oscillatory E-I Network
- Entertainment, Synchronization, and Oscillations
- Entertainment by Excitatory Input Pulses
- Synchronization by Fast Recurrent Excitation
- Phase Response Curves (PRCs)
- Synchronization of Two Pulse-coupled Oscillators
- Oscillators Coupled by Delayed Pulses
- Weakly Coupled Oscillators
- Approximate Synchronization by a Single Inhibitory Pulse
- The PING Model of Gamma Rhythms
- ING Rhythms
- Weak PING Rhythms
- Beta Rhythms
- Nested Gamma-theta Rhythms
- Functional Significance of Synchrony and Oscillations
- Rhythmic vs. Tonic Inhibition
- Rhythmic vs. Tonic Excitation
- Gamma Rhythms and Cell Assemblies
- Gamma Rhythms and Communication
- Synaptic Plasticity
- Short-term Depression and Facilitation
- Spike Timing-dependent Plasticity (STDP)
- Appendices
- A. The Bisection Method
- Fixed Point Iteration
- Elementary Probability Theory
- Smooth Approximations of Non-smooth Functions
- Solutions to Selected Homework Problems.
