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