State-Switching Damped Harmonic Oscillator Model

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.