An Introduction to Modeling Neuronal Dynamics. 1st ed. 2017

種類:

電子ブック

責任表示:

by Christoph Börgers

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Börgers, Christoph.
• SpringerLink (Online service)

シリーズ名:

Texts in Applied Mathematics ; 66

ISBN:

9783319511719 [3319511718]    

注記:

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) -- Syn
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 more than enough mathematical background. Only a slim, high school-level background in physics is assumed, and none in biology. Topics include models of individual nerve cells and their dynamics, models of networks of neurons coupled by synapses and gap junctions, origins and functions of population rhythms in neuronal networks, and models of synaptic plasticity. An extensive online collection of Matlab programs generating the figures accompanies the book. .

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