Dynamical Systems in Neuroscience The Geometry of Excitability and Bursting

ISBN-10: 0262514206
ISBN-13: 9780262514200
Edition: 2010
List price: $40.00 Buy it from $33.08
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Book details

List price: $40.00
Copyright year: 2010
Publisher: MIT Press
Publication date: 1/22/2010
Binding: Paperback
Pages: 464
Size: 6.75" wide x 10.00" long x 1.00" tall
Weight: 1.496
Language: English

Preface
Introduction
Neurons
What Is a Spike?
Where Is the Threshold?
Why Are Neurons Different, and Why Do We Care?
Building Models
Dynamical Systems
Phase Portraits
Bifurcations
Hodgkin Classification
Neurocomputational properties
Building Models (Revisited)
Review of Important Concepts
Bibliographical Notes
Electrophysiology of Neurons
Ions
Nernst Potential
Ionic Currents and Conductances
Equivalent Circuit
Resting Potential and Input Resistance
Voltage-Clamp and I-V Relation
Conductances
Voltage-Gated Channels
Activation of Persistent Currents
Inactivation of Transient Currents
Hyperpolarization-Activated Channels
The Hodgkin-Huxley Model
Hodgkin-Huxley Equations
Action Potential
Propagation of the Action Potentials
Dendritic Compartments
Summary of Voltage-Gated Currents
Review of Important Concepts
Bibliographical Notes
Exercises
One-Dimensional Systems
Electrophysiological Examples
I-V Relations and Dynamics
Leak + Instantaneous INa, p
Dynamical Systems
Geometrical Analysis
Equilibria
Stability
Eigenvalues
Unstable Equilibria
Attraction Domain
Threshold and Action Potential
Threshold and Action Potential
Bistability and Hysteresis
Phase Portraits
Topological Equivalence
Local Equivalence and the Hartman-Grobman Theorem
Bifurcations
Saddle-Node (Fold) Bifurcation
Slow Transition
Bifurcation Diagram
Bifurcations and I-V Relations
Quadratic Integrate-and-Fire Neuron
Review of Important Concepts
Bibliographical Notes
Exercises
Two-Dimensional Systems
Planar Vector Fields
Nullclines
Trajectories
Limit Cycles
Relaxation Oscillators
Equilibria
Stability
Local Linear Analysis
Eigenvalues and Eigenvectors
Local Equivalence
Classification of Equilibria
Example: FitzHugh-Nagumo Model
Phase Portraits
Bistability and Attraction Domains
Stable/Unstable Manifolds
Homoclinic/Heteroclinic Trajectories
Saddle-Node Bifurcation
Andronov-Hopf Bifurcation
Review of Important Concepts
Bibliographical Notes
Exercises
Conductance-Based Models and Their Reductions
Minimal Models
Amplifying and Resonant Gating Variables
INa,p+IK -Model
INa,t -Model
INa, p+Ih -Model
Ih+IKir -Model
IK+IKir -Model
IA -Model
Ca2+ -Gated Minimal Models
Reduction of Multidimensional Models
Hodgkin-Huxley model
Equivalent Potentials
Nullclines and I-V Relations
Reduction to Simple Model
Review of Important Concepts
Bibliographical Notes
Exercises
Bifurcations
Equilibrium (Rest State)
Saddle-Node (Fold)
Saddle-Node on Invariant Circle
Supercritical Andronov-Hopf
Subcritical Andronov-Hopf
Limit Cycle (Spiking State)
Saddle-Node on Invariant Circle
Supercritical Andronov-Hopf
Fold Limit Cycle
Homoclinic
Other Interesting Cases
Three-Dimensional Phase Space
Cusp and Pitchfork
Bogdanov-Takens
Relaxation Oscillators and Canards
Bautin
Saddle-Node Homoclinic Orbit
Hard and Soft Loss of Stability
Bibliographical Notes
Exercises
Neuronal Excitability
Excitability
Bifurcations
Hodgkin's Classification
Classes 1 and 2
Class 3
Ramps, Steps, and Shocks
Bistability
Class 1 and 2 Spiking
Integrators vs. Resonators
Fast Subthreshold Oscillations
Frequency Preference and Resonance
Frequency Preference in Vivo
Thresholds and Action Potentials
Threshold Manifolds
Rheobase
Postinhibitory Spike
Inhibition-Induced Spiking
Spike Latency
Flipping from an Integrator to a Resonator
Transition Between Integrators and Resonators
Slow Modulation
Spike Frequency Modulation
I-V Relation
Slow Subthreshold Oscillation
Rebound Response and Voltage Sag
AHP and ADP
Review of Important Concepts
Bibliographical Notes
Exercises
Simple Models
Simplest Models
Integrate-and-Fire
Resonate-and-Fire
Quadratic Integrate-and-Fire
Simple Model of Choice
Canonical Models
Cortex
Regular Spiking (RS) Neurons
Intrinsically Bursting (IB) Neurons
Multi-Compartment Dendritic Tree
Chattering (CH) Neurons
Low-Threshold Spiking (LTS) Interneurons
Fast Spiking (FS) Interneurons
Late Spiking (LS) Interneurons
Diversity of Inhibitory Interneurons
Thalamus
Thalamocortical (TC) Relay Neurons
Reticular Thalamic Nucleus (RTN) Neurons
Thalamic Interneurons
Other Interesting Cases
Hippocampal CA1 Pyramidal Neurons
Spiny Projection Neurons of Neostriatum and Basal Ganglia
Mesencephalic V Neurons of Brainstream
Stellate Cells of Entorhinal Cortex
Mital Neurons of the Olfactory Bulb
Review of Important Concepts
Bibliographical Notes
Exercises
Bursting
Electrophysiology
Example: The INa,p+IK+IK(M)-Model
Fast-Slow Dynamics
Minimal Models
Central Pattern Generators and Half-Center Oscillators
Geometry
Fast-Slow Bursters
Phase Portraits
Averaging
Equivalent Voltage
Hysteresis Loops and Slow Waves
Bifurcations �Resting Bursting Tonic Spiking�
Classification
Fold/Homoclinic
Circle/Circle
Fold/Fold Cycle
Fold/Hopf
Fold/Circle
Neurocomputational Properties
How to Distinguish?
Integrators vs. Resonators
Bistability
Bursts as a Unit of Neuronal Information
Chirps
Synchronization
Review of Important Concepts
Bibliographical Notes
Exercises
Synchronization
Solutions to Exercises
References
Index
Synchronization (www.izhikevich.com)
Pulsed Coupling
Phase of Oscillation
Isochrons
PRC
Type 0 and Type 1 Phase Response
Poincare Phase Map
Fixed Points
Synchronization
Phase-Locking
Arnold Tongues
Weak Coupling
Winfree's Approach
Kuramoto's Approach
Malkin's Approach
Measuring PRCs Experimentally
Phase Model for Coupled Oscillators
Synchronization
Two Oscillators
Chains
Networks
Mean-Field Approximations
Examples
Phase Oscillators
SNIC Oscillators
Homoclinic Oscillators
Relaxation Oscillators and FTM
Bursting Oscillators
Review of Important Concepts
Bibliographical Notes
Solutions

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