In this paper, we focus on the emergence of diverse neuronal oscillations arising in a mixed population of neurons with different excitability properties. These properties produce mixed mode oscillations (MMOs) characterized by the combination of large amplitudes and alternate subthreshold or small amplitude oscillations. Considering the biophysically plausible, Izhikevich neuron model, we demonstrate that various MMOs, including MMBOs (mixed mode bursting oscillations) and synchronized tonic spiking appear in a randomly connected network of neurons, where a fraction of them is in a quiescent (silent) state and the rest in self-oscillatory (firing) states. We show that MMOs and other patterns of neural activity depend on the number of oscillatory neighbors of quiescent nodes and on electrical coupling strengths. Our results are verified by constructing a reduced-order network model and supported by systematic bifurcation diagrams as well as for a small-world network. Our results suggest that, for weak couplings, MMOs appear due to the de-synchronization of a large number of quiescent neurons in the networks. The quiescent neurons together with the firing neurons produce high frequency oscillations and bursting activity. The overarching goal is to uncover a favorable network architecture and suitable parameter spaces where Izhikevich model neurons generate diverse responses ranging from MMOs to tonic spiking.

中文翻译：

---

不同可兴奋神经元随机网络中混合模式振荡的出现：邻居和电耦合的作用

在本文中，我们关注在具有不同兴奋性的混合神经元群中出现的不同神经元振荡。这些特性产生混合模式振荡 (MMO)，其特征是结合了大振幅和交替亚阈值或小振幅振荡。考虑到生物物理学上合理的 Izhikevich 神经元模型，我们证明了各种 MMO，包括 MMBO（混合模式突发振荡）和同步强直尖峰出现在随机连接的神经元网络中，其中一部分处于静止（静默）状态和其余处于自振荡（发射）状态。我们表明 MMO 和其他神经活动模式取决于静止节点的振荡邻居数量和电耦合强度。我们的结果通过构建降阶网络模型得到验证，并得到系统分叉图和小世界网络的支持。我们的结果表明，对于弱耦合，MMO 的出现是由于网络中大量静止神经元的不同步。静止神经元与放电神经元一起产生高频振荡和爆发性活动。首要目标是发现一个有利的网络架构和合适的参数空间，在这些空间中，Izhikevich 模型神经元产生从 MMO 到强效脉冲的各种响应。MMO 的出现是由于网络中大量静止神经元的不同步。静止神经元与放电神经元一起产生高频振荡和爆发性活动。首要目标是发现一个有利的网络架构和合适的参数空间，在这些空间中，Izhikevich 模型神经元产生从 MMO 到强效脉冲的各种响应。MMO 的出现是由于网络中大量静止神经元的不同步。静止神经元与放电神经元一起产生高频振荡和爆发性活动。首要目标是发现一个有利的网络架构和合适的参数空间，在这些空间中，Izhikevich 模型神经元产生从 MMO 到强效脉冲的各种响应。