A Linear Analysis of Coupled Wilson-Cowan Neuronal Populations

Neves L.L.; Monteiro L.H.A.

A Linear Analysis of Coupled Wilson-Cowan Neuronal Populations

Tipo

Artigo

Data de publicação

2016

Periódico

Computational Intelligence and Neuroscience

Citações (Scopus)

7

Autores

Neves L.L.
Monteiro L.H.A.

Resumo

© 2016 L. L. Neves and L. H. A. Monteiro.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.

Assuntos Scopus

Analytical results , Chaotic attractors , Equilibrium point , First order nonlinear differential equations , Fourth-order dynamical systems , Linear approximations , Neuronal populations , Sigmoidal functions , Animals , Computer Simulation , Humans , Linear Models , Models, Neurological , Nerve Net , Neurons