Rulkov map

The Rulkov map is a two-dimensional iterated map used to model a biological neuron. It was proposed by Nikolai F. Rulkov in 2001. The use of this map to study neural networks has computational advantages because the map is easier to iterate than a continuous dynamical system. This saves memory and simplifies the computation of large neural networks.

The model

The Rulkov map can be represented by following dynamical equations:

$x_{n+1}={\frac {\alpha }{1+x_{n}^{2}}}+y_{n}$

$y_{n+1}=y_{n}-\mu (x_{n}-\sigma )$

See also

• Biological neuron model
• Hodgkin–Huxley model
• FitzHugh–Nagumo model