论文标题
神经元种群中的连贯共振：平均场与网络模型
Coherence resonance in neuronal populations: mean-field versus network model
论文作者
论文摘要
相干共振的违反直觉现象描述了令人兴奋的政权中噪声诱导的振荡规则性的非单调性行为，从而在中间噪声强度的激发振荡的规律性方面产生了最佳响应。我们研究了具有不同耦合体系结构的Fitzhugh-Nagumo（FHN）神经元种群中的这种现象。对于FHN系统中的FHN系统网络，先前已经对连贯的共振进行了数值分析。在这里，我们着重于研究本地和全球耦合种群的平均场地限制的分析方法。平均场限制是指复杂网络的平均行为，因为元素的数量流向无穷大。我们得出一个近似于低噪声强度的本地耦合FHN网络的平均场极限。此外，我们将平均场方法应用于全球耦合的FHN网络。我们比较了平均场和网络框架的结果，以进行连贯共振，并在全球耦合的情况下找到良好的一致性，在这种情况下，两种方法之间的对应关系足以捕获抗蛋白谐振的出现。最后，我们研究了网络和平均场模型的耦合强度和噪声强度对相干共振的影响。
The counter-intuitive phenomenon of coherence resonance describes a non-monotonic behavior of the regularity of noise-induced oscillations in the excitable regime, leading to an optimal response in terms of regularity of the excited oscillations for an intermediate noise intensity. We study this phenomenon in populations of FitzHugh-Nagumo (FHN) neurons with different coupling architectures. For networks of FHN systems in excitable regime, coherence resonance has been previously analyzed numerically. Here we focus on an analytical approach studying the mean-field limits of the locally and globally coupled populations. The mean-field limit refers to the averaged behavior of a complex network as the number of elements goes to infinity. We derive a mean-field limit approximating the locally coupled FHN network with low noise intensities. Further, we apply mean-field approach to the globally coupled FHN network. We compare the results of the mean-field and network frameworks for coherence resonance and find a good agreement in the globally coupled case, where the correspondence between the two approaches is sufficiently good to capture the emergence of anticoherence resonance. Finally, we study the effects of the coupling strength and noise intensity on coherence resonance for both the network and the mean-field model.
