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Dynamical systems in neuroscience : the geometry of excitability and bursting / Eugene M. Izhikevich. — Cambridge, Mass. ; London : MIT Press, c2007. – (59.59/I98) |
Contents
Contents
Preface
1 Introduction
1.1 Neurons
1.2 Dynamical Systems
Review of Important Concepts
Bibliographical Notes
2 Electrophysiology of Neurons
2.1 Ions
2.2 Conductances
2.3 Tile Hodgkin-Huxley Model
Review of Important Concepts
Bibliographical Notes
Exercises
3 One-Dimensional Systems
3.1 Electrophysiological Examples
3.2 Dynamical Systems
3.3 Phase Portraits
Review of important Concepts
Bibliographical Notes
Exercises
4 Two-Dimensional Systems
4.1 Planar Vector Fields
4.2 Equilibria
4.3 Phase Portraits
Review of Important Concepts
Bibliographical Notes
Exercises
5 Conductance-Based Models and Their Reductions
5.1 Minimal Models
5.2 Reduction of Multidimensional Models
Review of important Concepts
Bibliographical Notes
Exercises
6 Bifurcations
6.1 Equilibrium (Rest State)
6.2 Limit Cycle (Spiking State)
6.3 Other Interesting Cases
Bibliographical Notes
Exercises
7 Neuronal Excitability
7.1 Excitability
7.2 Integrators vs. Resonators
7.3 Slow Modulation
Review of Important Concepts
Bibliographical Notes
Exercises
8 Simple Models
8.1 Simplest Models
8.2 Cortex
8.3 Thalamus
8.4 Other Interesting Cases
Review of Important Concepts
Bibliographical Notes
Exercises
9 Bursting
9.1 Electrophysiology
9.2 Geometry
9.3 Classification
9.4 Neurocomputational Properties
Review of Important Concepts
Bibliographical Notes
Exercises
10 Synchronization
Solutions to Exercises
References
Index
10 Synchronization (www.izhikevich.com)
10.1 Pulsed Coupling
10.2 Weak Coupling
10.3 Synchronization
10.4 Examples
Review of important Concepts
Bibliographical Notes
Solutions
