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