Hysteresis in coupled pair of Wilson-Cowan neuronal populations
The Wilson-Cowan model for the dynamics of coupled excitatory and inhibitory neuron populations was modified to incorporate coupling between two neuronal patches. Parameters for the model were chosen to exhibit hysteretic behavior. The activity of the excitatory and inhibitory subpopulations for both patches was then investigated under sinusoidal inputs and varying coupling strengths. Generally, the hysteresis loops shifted to the left as the coupling strength between the two patches was increased, making it more likely to enter a state of sustained excitation through a wider range of input values. For an appropriate choice of input, the stimulated patch can alternate between a highly excited state and a depression from resting activity. When the coupling strength is less than 1, the neighboring patch remains highly excited for all values of P. Otherwise, its behavior was found to be similar to the stimulated patch. Physiological interpretations were provided for each of the dynamical behaviors observed in the model.