# 28. Oscillations in Reverberating Loops

Oscillations in reverberating loops can be simplified and researched.

## Outlines

- Biological neuron networks have reverberating loops; inferior olive (IO).
- Periodic large-amplitude oscillations can happen even with each individual neurons firing at a significantly smaller rate or of irregular spike trains. Nicely explained in Fig. 8.11
- Strong oscillations with irregular spike trains is related to short-term memory and timing tasks.
- Binary neurons: potential of the ith neuron at time $t_{n+1}$ is determined by the states of other neurons at time $t_n$ $u_i(t_{n+1})=w_{ij}S_j(t_n)$. The state of neuron $S_i(t_n)$ is determined by the potential at time $t_{n}$, $S_i(t_n)=\Theta(u_i(t_n)-\theta)$, where $\theta$ is threshold.
- Approximate SRM to McClulloch-Pitts neurons with “digitized” states.
- For sparsely connect we can approximate the time evolution using independent events and find the probability.
- Fig. 8.12; The interactions are shown on the top panels. We start from a value of $a_n$, the iteration gives us the result of $a_{n+1}$. Then the next step depends on the value of $a_{n+1}$ so we project it onto the dashed line $a_{n}=a_{n+1}$. Then we use the new $a_n$ value to find the new $a_{n+1}$.

### Excitations and Inhibitions

- Random network with balanced excitations and inhibitions can generate broad interval distributions.
- Reverberating projections usually have both excitation and inhibitions.
- McClulloch-Pitts model with both excitations and inhibitions.

### Microscopic Dynamics

- The simplified model (SRM->McClulloch-Pitts) doesn’t catch all the features, with inhibitory neurons in presence. The limit circle can grow substantially larger as size of the network increases.
- Information will drain away with noise. Fig. 8.15

Planted:
by OctoMiao;

## Table of Contents

**References:**

**Current Ref:**

- snm/28.oscillations-in-reverberating-loops.md