I am attempting to simulate a network of four neurons, where the `i`

th neuron’s dynamics are described by the following differential equations:

where \tau_{us} >> \tau_{s} >> 1, and

The network is entirely homogeneous, where each neuron has the same parameters, and all of the weights between the neurons are the same.

I am using Lsoda and DifferentialEquations.JL to solve the system, with reltol = abstol = 1e-8. I find that the system either immediately converges to a fixed point or a limit cycle depending on the time span over which I integrate. Any suggestions as to why this is happening and how I might fix it would be appreciated.