A Linear Analysis of Coupled Wilson-Cowan Neuronal Populations

Abstract EN

Let a neuronal population be composed of an excitatory group interconnected to an inhibitory group.

In the Wilson-Cowan model, the activity of each group of neurons is described by a first-order nonlinear differential equation.

The source of the nonlinearity is the interaction between these two groups, which is represented by a sigmoidal function.

Such a nonlinearity makes difficult theoretical works.

Here, we analytically investigate the dynamics of a pair of coupled populations described by the Wilson-Cowan model by using a linear approximation.

The analytical results are compared to numerical simulations, which show that the trajectories of this fourth-order dynamical system can converge to an equilibrium point, a limit cycle, a two-dimensional torus, or a chaotic attractor.

The relevance of this study is discussed from a biological perspective.