Hopfield Brody synchronization (sync) model

Individual units are integrate-and-fire neurons.

How it works

The synchronization mechanism requires that all of the cells fire spontaneously at similar frequencies. It is obvious that if all cells are started at the same time, they will still be roughly synchronous after one cycle (since they have similar intrinsic cycle periods). After two cycles, they will have drifted further apart. After many cycles, differences in period will be magnified, leading to no temporal relationship of firing.

The key observation utilized here is that firing is fairly synchronized one cycle after onset. The trick is to reset the cells after each cycle so that they start together again. They then fire with temporal differences equal to the differences in their intrinsic periods. This resetting can be provided by an inhibitory input which pushes state variable m down far from threshold (hyperpolarized, as it were). This could be accomplished through an external pacemaker that reset all the cells, thereby imposing the external frequency onto the network. The interesting observation in this network is that pacemaking can also be imposed from within, though an intrinsic connectivity that enslaves all members to the will of the masses.

Exercises to gain familiarity

Beyond the GUI -- Saving and displaying spikes

Synchronization measures

Procedure interval2() in ocomm.hoc sets cell periods randomly

Rewiring the network

All of the programs that I used in my presentation are available in ocomm.hoc. The student may wish to use or rewrite any of these procedures. Below I suggest a different approach to wiring the network.

Assessing connectivity

Graphing connectivity

Animate