Point Neurons
Morris-Lecar Neuron
Exhibiting a supercritical Hopf bifurcation.
Morris-Lecar Neuron
Exhibiting a saddle-node bifurcation on a limit cycle.
Hodgkin-Huxley Neuron
Exhibiting co-existing limit-cycles and fixed points.
Regular-Spiking Neuron
In a minimal Hodgkin-Huxley model (Pospischil et al, 2008).
Hindmarsh-Rose Neuron
Intrinsic spike bursting.
Fitzhugh-Nagumo Neuron
Exhibiting action potential prolongation.
Neural Masses
Wilson-Cowan
Excitatory-Inhibitory populations.
Breakspear-Terry-Friston
Exhibiting deterministic chaos
Heitmann-Ermentrout
E-I-E model of perceptual opponency
Spatial Models
Fitzhugh-Nagumo
Initiation of spiral rotors
Fitzhugh-Nagumo
Arrhythmogenesis in cardiac tissue
Normal Forms
Hopf Bifurcation
Normal form of the Hopf bifurcation.
SNLC Bifurcation
Normal form of the saddle-node bifurcation on a limit cycle (SNLC).
Classics
Lorenz Attractor
Deterministic chaos.
Damped & Driven Pendulum
Cylindrical coordinates.
Wave Equation
Reflecting boundaries.
Arithmetic Brownian Motion
Drift and Diffusion.
Geometric Brownian Motion
Mathematical Finance
Van Der Pol Oscillator
Relaxation Oscillator