Implementing a simple harmonic oscillator (Eq 13) using a recurrent connection.

Using the network architecture in Fig 5, we initialize neural populations “pop1” and “pop2” with 100 detailed neurons, then use osNEF to train encoders, decoders, and synaptic filters. The connection between “pop1” and “pop2” is trained to compute Eq 13. The weights and synapses from this trained model are then substituted into a testing network, shown in Fig 8. The top panel shows the state space target and the decoded estimates from “pop2”, with a break in the x-axis to show that oscillations remain stable over 100 seconds. The bottom panel show the mean error between this estimate and a best-fit sinuoid, as well as the frequency error between this best-fit sinusoid and the target frequency ω = 2π.