A method for detecting false bifurcations in dynamical systems: application to neural-field models.
A method for detecting false bifurcations in dynamical systems: application to neural-field models.
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一种检测动态系统中假分叉的方法：在神经场模型中的应用。
DOI：
10.1007/s00422-009-0357-y
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发表时间：
2010
影响因子：
1.9
通讯作者：
Rodrigues S
中科院分区：
文献类型：
--
作者：
Rodrigues S
在这篇文章中，我们提出了一种跟踪由于拐点引起的极限环解曲率变化的方法。为了与以前的文献保持一致，我们将这些变化称为假分岔，因为当考虑与解相切的庞卡罗剖面时，它们看起来是分岔，但实际上，随着参数的变化，解的变形会平滑地发生。这些类型的解决方案通常出现在失神癫痫发作的脑电图模型中，并对应于这些模型中峰的形成。在参数空间中跟踪这些转换，可以根据不同类型的尖峰和波动动力学来定义相应的区域，这可能在临床神经科学中用作对更一般综合征的不同亚型进行分类的手段。
In this article, we present a method for tracking changes in curvature of limit cycle solutions that arise due to inflection points. In keeping with previous literature, we term these changes false bifurcations, as they appear to be bifurcations when considering a Poincaré section that is tangent to the solution, but in actual fact the deformation of the solution occurs smoothly as a parameter is varied. These types of solutions arise commonly in electroencephalogram models of absence seizures and correspond to the formation of spikes in these models. Tracking these transitions in parameter space allows regions to be defined corresponding to different types of spike and wave dynamics, that may be of use in clinical neuroscience as a means to classify different subtypes of the more general syndrome.