Universidade Presbiteriana Mackenzie, Escola de Engenharia, São Paulo, SP, Brazil.
Universidade Presbiteriana Mackenzie, Escola de Engenharia, São Paulo, SP, Brazil; Universidade de São Paulo, Escola Politécnica, São Paulo, SP, Brazil.
Comput Intell Neurosci. 2016;2016:8939218. doi: 10.1155/2016/8939218. Epub 2016 Sep 20.
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.
让一个神经元群体由一个兴奋性群体和一个抑制性群体相互连接组成。在威尔逊-考恩模型中，每个神经元群体的活动由一个一阶非线性微分方程来描述。这种非线性的来源是这两个群体之间的相互作用，它由一个 sigmoidal 函数来表示。这种非线性使得理论工作变得困难。在这里，我们通过使用线性逼近的方法，对由威尔逊-考恩模型描述的一对耦合群体的动力学进行了分析研究。分析结果与数值模拟进行了比较，结果表明，这个四阶动力系统的轨迹可以收敛到一个平衡点、一个极限环、一个二维环面或一个混沌吸引子。从生物学的角度讨论了这项研究的相关性。
