A Linear Analysis of Coupled Wilson-Cowan Neuronal Populations. (20th September 2016)

• Record Type: Journal Article
• Authors: Neves, L. L.; Monteiro, L. H. A.
• Other Names: Sanei Saeid Academic Editor.
• Is Part Of: Computational intelligence and neuroscience. Volume 2016(2016)
• Publication Date: 2016-09-20
• Subjects: Neurosciences -- Data processing -- Periodicals; Computational intelligence -- Periodicals; Computational neuroscience -- Periodicals; 612.80285
• DOI: 10.1155/2016/8939218
• Languages: English
• ISSNs: 1687-5265

Abstract

Abstract : 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.