Interaction of Canard and Singular Hopf Mechanisms in a Neural Model
Interaction of Canard and Singular Hopf Mechanisms in a Neural Model
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DOI：
10.1137/110823171
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发表时间：
2011-01-01
影响因子：
2.1
通讯作者：
Rubin, J.
中科院分区：
文献类型：
--
作者：
Curtu, R.;Rubin, J.
我们考虑之前在双眼竞争研究中提出的神经竞争常微分方程模型，其特征是两个适应的神经元群体通过相互抑制相互作用。众所周知，该模型表现出多种动态状态，包括混合模式振荡 (MMO)，其特征是根据输入参数的值交替出现小振幅和大幅振荡。在这项工作中，我们使用几何动力系统技术来研究奇异极限下的模型结构以及扰动系统中 MMO 的出现。特别是，利用范式计算允许我们以数值方式计算出路函数，我们用它来阐明鸭式和奇异 Hopf 机制在输入参数接近临界值时发生的小幅度振荡的相互作用。
We consider an ordinary differential equation model for neural competition, presented previously in the study of binocular rivalry, which features two adapting populations of neurons interacting through mutual inhibition. This model is known to exhibit a variety of dynamic regimes, including mixed-mode oscillations (MMOs) featuring alternating small-and large amplitude oscillations, depending on the value of an input parameter. In this work, we use geometric dynamical systems techniques to study the structure of the model in the singular limit as well as the emergence of MMOs in the perturbed system. In particular, exploiting a normal form calculation allows us to numerically compute a way-in/way-out function, which we use to elucidate the interaction of canard and singular Hopf mechanisms for small amplitude oscillations that occur as the input parameter approaches a critical value.