论文标题
超越威尔逊 - 牛肉动力学：振荡和混乱而没有抑制作用
Beyond Wilson-Cowan dynamics: oscillations and chaos without inhibition
论文作者
论文摘要
五十年前，威尔逊和考恩开发了一种数学模型来描述神经种群的活性。在这项开创性的工作中，他们将细胞分为三组：主动，敏感和难治性，并获得了一个动力学系统来描述种群平均发射速率的演变。在目前的工作中，我们研究了经常被忽视的耐火状态的影响，并表明考虑到它可以引入新的动态。从连续的马尔可夫链开始，我们对平均场模型进行了严格的推导，该模型包括种群的难治部分作为动态变量。然后，我们进行分叉分析，以解释在经典的威尔逊 - 牛群无法预测振荡的情况下，周期性解决方案的发生。我们还表明，我们的平均场模型能够预测仅两个人群的网络动力学中的混乱行为。
Fifty years ago, Wilson and Cowan developed a mathematical model to describe the activity of neural populations. In this seminal work, they divided the cells in three groups: active, sensitive and refractory, and obtained a dynamical system to describe the evolution of the average firing rates of the populations. In the present work, we investigate the impact of the often neglected refractory state and show that taking it into account can introduce new dynamics. Starting from a continuous-time Markov chain, we perform a rigorous derivation of a mean-field model that includes the refractory fractions of populations as dynamical variables. Then, we perform bifurcation analysis to explain the occurance of periodic solutions in cases where the classical Wilson-Cowan does not predict oscillations. We also show that our mean-field model is able to predict chaotic behavior in the dynamics of networks with as little as two populations.
