School of Mathematical and Computational Sciences, Massey University, Private Bag 102-904 NSMC, Auckland, New Zealand.
Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476, Potsdam, Germany.
Biol Cybern. 2023 Oct;117(4-5):259-274. doi: 10.1007/s00422-023-00969-6. Epub 2023 Aug 3.
We consider a next generation neural field model which describes the dynamics of a network of theta neurons on a ring. For some parameters the network supports stable time-periodic solutions. Using the fact that the dynamics at each spatial location are described by a complex-valued Riccati equation we derive a self-consistency equation that such periodic solutions must satisfy. We determine the stability of these solutions, and present numerical results to illustrate the usefulness of this technique. The generality of this approach is demonstrated through its application to several other systems involving delays, two-population architecture and networks of Winfree oscillators.
我们考虑了下一代神经场模型，该模型描述了环形上θ神经元网络的动力学。对于某些参数，网络支持稳定的时间周期性解。利用每个空间位置的动力学由复值Riccati 方程描述的事实，我们推导出这样的周期性解必须满足的自洽方程。我们确定了这些解的稳定性，并给出了数值结果来说明该技术的有效性。通过将该方法应用于涉及延迟、两群结构和Winfree 振荡器网络的几个其他系统，证明了该方法的通用性。
