An Introduction to Dynamical Systems and Neuronal Dynamics View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2005

AUTHORS

Alla Borisyuk , Avner Friedman , Ermentrout , David Terman

ABSTRACT

1. Introduction 2. One Dimensional Equations 2.1. The Geometric Approach 2.2. Bifurcations 2.3. Bistability and Hysteresis 3. Two Dimensional Systems 3.1. The Phase Plane 3.2. An Example 3.3. Oscillations 3.4. Local Bifurcations 3.5. Global Bifurcations 3.6. Geometric Singular Perturbation Theory 4. Single Neurons 4.1. Some Biology 4.2. The Hodgkin-Huxley Equations 4.3. Reduced Models 4.4. Bursting Oscillations 4.5. Traveling Wave Solutions 5. Two Mutually Coupled Cells 5.1. Introduction 5.2. Synaptic Coupling 5.3. Geometric Approach 5.4. Synchrony with Excitatory Synapses 5.5. Desynchrony with Inhibitory Synapses 6. Activity Patterns in the Basal Ganglia 6.1. Introduction 6.2. The Basal Ganglia 6.3. The Model 6.4. Activity Patterns 6.5. Concluding Remarks References More... »

PAGES

21-68

Book

TITLE

Tutorials in Mathematical Biosciences I

ISBN

978-3-540-23858-4
978-3-540-31544-5

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-540-31544-5_2

DOI

http://dx.doi.org/10.1007/978-3-540-31544-5_2

DIMENSIONS

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