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Tutorials in Mathematical Biosciences I: Mathematical Neuroscience

Alla Borisyuk Avner Friedman Bard Ermentrout David Terman

Resumen/Descripción – provisto por la editorial

No disponible.

Palabras clave – provistas por la editorial

Mathematical and Computational Biology; Ordinary Differential Equations; Partial Differential Equations; Computational Mathematics and Numerical Analysis; Neurobiology; Computer Appl. in Life Sciences

Disponibilidad
Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2005 SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-3-540-23858-4

ISBN electrónico

978-3-540-31544-5

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Springer-Verlag Berlin Heidelberg 2005

Tabla de contenidos

Introduction to Neurons

Avner Friedman

1. The Structure of Cells 2. Nerve Cells 3. Electrical Circuits and the Hodgkin-Huxley Model 4. The Cable Equation References

Pp. 1-20

An Introduction to Dynamical Systems and Neuronal Dynamics

David Terman

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

Pp. 21-68

Neural Oscillators

Bard Ermentrout

1. Introduction 2. How Does Rhythmicity Arise 3. Phase-Resetting and Coupling Through Maps 4. Doublets, Delays, and More Maps 5. Averaging and Phase Models 5.1. Local Arrays 6. Neural Networks 6.1. Slow Synapses 6.2. Analysis of the Reduced Model 6.3. Spatial Models References

Pp. 69-106

Physiology and Mathematical Modeling of the Auditory System

Alla Borisyuk

1. Introduction 1.1. Auditory System at a Glance 1.2. Sound Characteristics 2. Peripheral Auditory System 2.1. Outer Ear 2.2. Middle Ear 2.3. Inner Ear. Cochlea. Hair Cells. 2.4. Mathematical Modeling of the Peripheral Auditory System 3. Auditory Nerve (AN) 3.1. AN Structure 3.2. Response Properties 3.3. How Is AN Activity Used by Brain? 3.4. Modeling of the Auditory Nerve 4. Cochlear Nuclei 4.1. Basic Features of the CN Structure 4.2. Innervation by the Auditory Nerve Fibers 4.3. Main CN Output Targets 4.4. Classifications of Cells in the CN 4.5. Properties of Main Cell Types 4.6. Modeling of the Cochlear Nuclei 5. Superior Olive. Sound Localization, Jeffress Model 5.1. Medial Nucleus of the Trapezoid Body (MNTB) 5.2. Lateral Superior Olivary Nucleus (LSO) 5.3. Medial Superior Olivary Nucleus (MSO) 5.4. Sound Localization. Coincidence Detector Model 6. Midbrain 6.1. Cellular Organization and Physiology of Mammalian IC 6.2. Modeling of the IPD Sensitivity in the Inferior Colliculus 7. Thalamus and Cortex References

Pp. 107-168