A two-processing element adaptable linear oscillating recurrent system with single-weight plasticity

A simple recursive linear two-processing element adaptable oscillator is developed and demonstrated. Simple harmonic motion and its mathematical description is the foundation of this study. State equations for an undamped spring-mass system are converted to a discrete time system, followed by eigenvalue analysis to convert the four-degree-of-freedom system to a recursive network with plasticity in one variable. The oscillator is initialized to a frequency in the neighborhood of the desired frequency, and tuned by using resilient backpropagation modified for backpropagation through time. It is shown that the network can track frequencies in a spectrum of operation as defined by the sampling frequency, given the network is initialized to frequencies in the neighborhood of those of interest.