Introduction to Modeling Neuronal Dynamics
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Introduction to Modeling Neuronal Dynamics
Boergers, Christoph
Springer International Publishing AG
07/2018
457
Mole
Inglês
9783319845852
15 a 20 dias
718
Descrição não disponível.
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.
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Single Neuron Models;Mathematical Modeling;Computational Neuroscience;Hodgkin-Huxley Equations;Differential Equations;Brain Rhythms;Synchronization;Dynamics
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.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
