title: A Linear Analysis of Coupled Wilson-Cowan Neuronal Populations.
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.
authors.affiliation: Universidade Presbiteriana Mackenzie, Escola de Engenharia, São Paulo, SP, Brazil.
authors.forename: L L
authors.initials: LL
authors.lastname: Neves
authors.affiliation: Universidade Presbiteriana Mackenzie, Escola de Engenharia, São Paulo, SP, Brazil; Universidade de São Paulo, Escola Politécnica, São Paulo, SP, Brazil.
authors.forename: L H A
authors.identifier: 0000-0003-2717-5241
authors.initials: LH
authors.lastname: Monteiro
mesh_terms: D000818:Animals; D003198:Computer Simulation; D006801:Humans; D016014:Linear Models; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*