Nicola Wilten, Hellyer Peter John, Campbell Sue Ann, Clopath Claudia
Department of Bioengineering, Imperial College London, London SW7 2AZ, United Kingdom.
Department of Applied Mathematics, University of Waterloo, 200 University Avenue W., Waterloo, Ontario N2L 3G1, Canada.
Chaos. 2018 Aug;28(8):083104. doi: 10.1063/1.5026489.
Low-dimensional yet rich dynamics often emerge in the brain. Examples include oscillations and chaotic dynamics during sleep, epilepsy, and voluntary movement. However, a general mechanism for the emergence of low dimensional dynamics remains elusive. Here, we consider Wilson-Cowan networks and demonstrate through numerical and analytical work that homeostatic regulation of the network firing rates can paradoxically lead to a rich dynamical repertoire. The dynamics include mixed-mode oscillations, mixed-mode chaos, and chaotic synchronization when the homeostatic plasticity operates on a moderately slower time scale than the firing rates. This is true for a single recurrently coupled node, pairs of reciprocally coupled nodes without self-coupling, and networks coupled through experimentally determined weights derived from functional magnetic resonance imaging data. In all cases, the stability of the homeostatic set point is analytically determined or approximated. The dynamics at the network level are directly determined by the behavior of a single node system through synchronization in both oscillatory and non-oscillatory states. Our results demonstrate that rich dynamics can be preserved under homeostatic regulation or even be caused by homeostatic regulation.
低维却丰富的动力学现象常常出现在大脑中。例子包括睡眠、癫痫和自主运动期间的振荡和混沌动力学。然而，低维动力学出现的一般机制仍然难以捉摸。在这里，我们考虑威尔逊 - 考恩网络，并通过数值和分析工作证明，网络 firing 率的稳态调节可能反常地导致丰富的动力学表现。当稳态可塑性在比 firing 率适度更慢的时间尺度上起作用时，动力学包括混合模式振荡、混合模式混沌和混沌同步。对于单个递归耦合节点、没有自耦合的相互耦合节点对以及通过从功能磁共振成像数据导出的实验确定权重进行耦合的网络来说都是如此。在所有情况下，稳态设定点的稳定性都通过解析确定或近似。网络层面的动力学直接由单个节点系统在振荡和非振荡状态下通过同步的行为决定。我们的结果表明，丰富的动力学可以在稳态调节下得以保留，甚至由稳态调节所导致。
