有限宽度脉冲存在下的集体动力学
Collective dynamics in the presence of finite-width pulses
AI总结：
本文研究有限脉冲宽度对兴奋性-抑制性相位振荡器网络集体动力学的影响，发现较宽抑制脉冲可引发带迟滞的同步转变，并平滑δ尖峰模型中的一阶相变。
摘要：
将神经元脉冲理想化为δ尖峰是神经科学中一种方便的方法，但有时会导致错误结论。我们研究有限脉冲宽度对平衡神经元网络动力学的影响。具体而言，我们研究由相同兴奋性和抑制性神经元两个群体组成的随机网络，其中相位振荡器通过具有不同宽度的指数脉冲耦合。我们考虑三种耦合函数，其灵感来自具有延迟和I型相位响应曲线的泄漏积分发放神经元。通过探究不同耦合强度下脉冲宽度的作用，我们发现稳健的集体不规则动力学；当抑制性脉冲比兴奋性脉冲足够宽时，该动力学会坍缩为完全同步状态。向同步的转变伴随迟滞现象（即集体不规则动力学与同步动力学共存）。我们的数值结果得到完全同步解的详细标度和稳定性分析支持。对于δ尖峰所推测出现的一阶相变，在有限宽度脉冲下被平滑化。
英文摘要：
The idealisation of neuronal pulses as $δ$-spikes is a convenient approach in neuroscience but can sometimes lead to erroneous conclusions. We investigate the effect of a finite pulse-width on the dynamics of balanced neuronal networks. In particular, we study two populations of identical excitatory and inhibitory neurons in a random network of phase oscillators coupled through exponential pulses with different widths. We consider three coupling functions, inspired by leaky integrate-and-fire neurons with delay and type-I phase-response curves. By exploring the role of the pulse-widths for different coupling strengths we find a robust collective irregular dynamics, which collapses onto a fully synchronous regime if the inhibitory pulses are sufficiently wider than the excitatory ones. The transition to synchrony is accompanied by hysteretic phenomena (i.e. the co-existence of collective irregular and synchronous dynamics). Our numerical results are supported by a detailed scaling and stability analysis of the fully synchronous solution. A conjectured first-order phase transition emerging for $δ$-spikes is smoothed out for finite-width pulses.
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