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Field name	Details
Dewey Class	519
Title	An Introduction to Modeling Neuronal Dynamics ([EBook]) / by Christoph Börgers.
Author	Börgers, Christoph
Other name(s)	SpringerLink (Online service)
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2017.
Physical Details	XIII, 457 p. 356 illus., 186 illus. in color. : online resource.
Series	Texts in applied mathematics 0939-2475 ; ; 66
ISBN	9783319511719
Summary Note	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. .:
Contents note	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) -- Synchronization of Two Pulse-coupled Oscillators -- Oscillators Coupled by Delayed Pulses -- Weakly Coupled Oscillators -- Approximate Synchronization by a Single Inhibitory Pulse -- The PING Model of Gamma Rhythms -- ING Rhythms -- Weak PING Rhythms -- Beta Rhythms -- Nested Gamma-theta Rhythms -- Functional Significance of Synchrony and Oscillations -- Rhythmic vs. Tonic Inhibition -- Rhythmic vs. Tonic Excitation -- Gamma Rhythms and Cell Assemblies -- Gamma Rhythms and Communication -- Synaptic Plasticity -- Short-term Depression and Facilitation -- Spike Timing-dependent Plasticity (STDP) -- Appendices -- A. The Bisection Method -- Fixed Point Iteration -- Elementary Probability Theory -- Smooth Approximations of Non-smooth Functions -- Solutions to Selected Homework Problems.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-319-51171-9
Links to Related Works	Subject References: Biomathematics . Dynamical Systems . Dynamics . Mathematical and Computational Biology . Mathematical Models of Cognitive Processes and Neural Networks . Mathematics . Neural networks (Computer science) . Neurosciences . Statistical Physics and Dynamical Systems . Vibration . Vibration, Dynamical Systems, Control . Authors: Börgers, Christoph . Corporate Authors: SpringerLink (Online service) . Series: Texts in applied mathematics . Classification: 519 .

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An Introduction to Modeling Neuronal Dynamics

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