Terman-Wang Oscillator NetworkTerman-Wang Oscillator Network
This description assumes that you are already familiar with the properties of the Terman-Wang oscillator (and have ideally used the wangNeuron MAD demonstration).
This demonstration simulates a network of four neural oscillators, which are connected via excitatory connections. In addition, each oscillator sends excitation to a global inhibitor, which feeds back inhibition to each cell in the network. The topology of the network is shown below:
When there are no excitatory weights between oscillators, inhibition from the global inhibitor causes the cells to desynchronize, so that the active phase of each occurs during a different time period. However, when oscillators are connected by mutual excitatory weights this offsets inhibition from the global inhibitor, and the oscillators tend to help each other to 'jump up' to the active phase. As a result, blocks of activity occur in the network, such that the oscillators within each block are synchronized, and different blocks are desynchronized.
Note: the colours in the weight matrix panel do not appear when running on some PCs under Matlab 5.2 (fixed under 5.3). This does not affect the demonstration.
The activity of the oscillator network is shown in the phase plane (1) and time domain (2). In the time domain plot (2), the activity of the global inhibitor is also shown as a black trace. Each oscillator is color coded, as shown in the network topology above. Similarly, excitatory weights between oscillators can be added or removed by clicking on the elements of the weight matrix (3). For example, in the diagram, there is an excitatory connection between blue and red, but no connection between blue and green. Note that it is not possible to connect an oscillator to itself.
It is possible to control the amount of input to, and feedback from, the global inhibitor by setting the slider marked WZ (4). The corresponding weight in the network is labelled in the network diagram above. You can also determine the initial conditions of the oscillators (6); all synchronized, all desynchronized or random synchronization.
Start a simulation by selecting the Begin simulation button (5). Some present simulations can also be accessed via the Preset menu.
1. Play with the value of WZ. A value of 0.5 will give behaviour similar to that described above, but what happens if you set it to zero? What happens if global inhibition is very large?
2. Watch the behaviour of the oscillators in the phase plane. When an oscillator jumps up to the active phase, you should see the others being pushed to the left (i.e., their x values are reduced because of the global inhibition induced by the oscillator that has just jumped).
D. Terman and D. L. Wang (1995) Global competition and local cooperation in a network of neural oscillators. Physica D, 81, pp. 148-176.
See also the demonstrations for the Terman-Wang neural oscillator (wangNeuron) and vowel segregation using neural oscillations (vowelSeg).
Produced by: Guy J. Brown
Release date: June 22 1998
Permissions: This demonstration may be used and modified freely by anyone. It may be distributed in unmodified form.
