小世界神经元网络的时空动力学：两种时滞耦合的作用
Spatiotemporal dynamics on small-world neuronal networks: The roles of two types of time-delayed coupling
摘要：
我们研究了由噪声Terman-Wang（TW）可兴奋神经元组成的小世界网络的时间相干性和空间同步性，依赖于两种类型的时间延迟耦合：$\{x_j(t-τ)-x_i (t)\}$和$\{x_j(t-τ)-x_i(t-τ)\}$。对于前一种情况下，我们表明，在耦合的时间延迟可以显着提高时间的连贯性和空间同步的噪声诱导的尖峰列车。此外，如果延迟时间$τ$被调谐到几乎匹配的神经网络的内在尖峰周期，系统动力学达到最有序的状态，这是在时间上的周期性和几乎同步的空间，展示了一个有趣的共振现象与延迟。对于后一种情况，然而，我们不能实现类似的时空有序状态，但神经元动力学表现出有趣的同步过渡与时间延迟从锯齿形的正面的激励，动态集群反相同步（APS），并进一步集群嵌合体状态具有空间分布的反相相干分离的不相干。此外，我们还展示了这些发现是如何受到噪声强度和重新布线概率的变化的影响。最后，对数值结果进行了定性分析.
英文摘要：
We investigate temporal coherence and spatial synchronization on small-world networks consisting of noisy Terman-Wang (TW) excitable neurons in dependence on two types of time-delayed coupling: $\{x_j(t-τ)-x_i (t)\}$ and $\{x_j(t-τ)-x_i(t-τ)\}$. For the former case, we show that time delay in the coupling can dramatically enhance temporal coherence and spatial synchrony of the noise-induced spike trains. In addition, if the delay time $τ$ is tuned to nearly match the intrinsic spike period of the neuronal network, the system dynamics reaches a most ordered state, which is both periodic in time and nearly synchronized in space, demonstrating an interesting resonance phenomenon with delay. For the latter case, however, we can not achieve a similar spatiotemporal ordered state, but the neuronal dynamics exhibits interesting synchronization transition with time delay from zigzag fronts of excitations to dynamic clustering anti-phase synchronization (APS), and further to clustered chimera states which have spatially distributed anti-phase coherence separated by incoherence. Furthermore, we also show how these findings are influenced by the change of the noise intensity and the rewiring probability. Finally, qualitative analysis is given to illustrate the numerical results.
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