The code provided is modeling a computational neuroscience phenomenon known as the Hopf bifurcation within the context of the Wilson-Cowan (WC) neural population model. This model is classically used to describe the dynamics of excitatory and inhibitory interactions within neural networks and provides insight into how these interactions can lead to various dynamic behaviors observed in brain activity.
Neural Populations:
E(t)
and I(t)
in the code represent the average firing rates or activity levels of these populations at time t
.Excitatory and Inhibitory Interactions:
WE
in the code signifies the strength of the excitatory connections. Different values (e.g., 1.9, 2.05, 2.115, 2.25) affect the network dynamics significantly, influencing stability and types of neural oscillations.Dynamic Behaviors and Oscillations:
WE
are adjusted, the model can transition through various regimes including steady-state behaviors, periodic oscillations, chaotic dynamics, and relaxation oscillations.Model Parameters:
tau1
and tau2
represent synaptic time constants for excitatory and inhibitory populations, which determine how quickly these populations can respond to inputs.p
, a
, alpha
, and theta
in the code are parameters influencing the non-linear interactions between neural populations, as well as the sigmoid function shaping the input-output relations.Simulations and Bifurcation Analysis:
This code simulates key aspects of neural population dynamics through the lens of the Wilson-Cowan model, emphasizing the role of bifurcations in generating various oscillatory and chaotic behaviors. These phenomena are crucial for understanding complex brain functions and disorders marked by abnormal oscillatory activity.