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.

我们考虑下一代神经场模型，它描述环上 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，我们推导了此类周期解必须满足的自洽方程。我们确定这些解决方案的稳定性，并提供数值结果来说明该技术的有用性。这种方法的通用性通过其在涉及延迟、二群架构和 Winfree 振荡器网络的其他几个系统中的应用得到了证明。