This Demonstration shows a continuous-time model of a single element,

, in a network. In the discrete version, each

can take the values of 0 or 1, and the elements are updated according to input from their neighbors. In the continuous description,

can take a continuum of values, but in order to approximate the discrete state the values should be close to either 0 or 1. This model implements a damped harmonic oscillator in which a function,

, determines when the oscillator switches between states 0 and 1, according to input from the neighbors.

is an indicator function that allows switching only when its

argument is positive. The specific form is

, where

is the transition length scale. Care must be taken in selecting the parameters so that accurate transitions occur between states.