Doi S., Inoue J., Pan Z., Tsumoto K. Computational Electrophysiology

Tokyo, Springer, 2010. - 157 p.The monograph is devoted to the consideration of electrical phenomena in a neuron from the standpoint of the theory of dynamical systems using the method of computer analysis of bifurcations. The classical Hodgkin-Huxley model and its generalizations are investigated. The processes in the heart muscle are considered. For neurophysiologists with a sufficient level of mathematical training.Contents
A Very Short Trip on Dynamical Systems
Difference Equations,Maps, and Linear Algebra
Differential Equations, Vector Fields, and Phase Planes
Linearization, Stabilities, Coordinate Transformation
Nonlinear Dynamical Systems and Bifurcations
Computational Bifurcation Analysis
The Hodgkin–Huxley Theory of Neuronal Excitation
What is a Neuron? Neuron is a Signal Converter
The Hodgkin–Huxley Formulation of Excitable Cell Membranes
Nonlinear Dynamical Analysis of the Original HH Equations
Computational and Mathematical Models of Neurons
Phase Plane Dynamics in the Context of Spiking Neuron
Simple Models of Neurons and Neuronal Oscillators
A Variant of the BVP Neuron Model
Shastic NeuronModels
Shastic Phase-Lockings and Bifurcations
Whole System Analysis of Hodgkin–Huxley Systems
Changing the Parameters: Sensitivity and Robustness
Bifurcations of the Hodgkin–Huxley Neurons
Two-Parameter Bifurcation Analysis of the HH Equations
Numerical Bifurcation Analysis by XPPAUT
Hodgkin–Huxley-Type Models of Cardiac Muscle Cells
Action Potentials in a Heart
Pacemaker Cell Model
Ventricular Cell Model
Other HH-TypeModels of Cardiac Cells