论文标题
全球耦合尖峰神经元网络网络的确切有限维描述
Exact finite-dimensional description for networks of globally coupled spiking neurons
论文作者
论文摘要
我们考虑了全球耦合尖峰神经元的大型网络，并在热力学极限中得出了其集体动力学的精确低维描述。单个神经元由ErmentRout-Kopell典型模型描述，可以激发或刺激性地尖峰，并通过脉冲与其他神经元相互作用。利用二次积分和射线和theta神经元公式的等效性，我们首先根据库拉莫托 - 达多订单参数（相位分布的傅立叶模式）来得出动态方程，并将它们与两个生物物理相关的宏观宏观观测观测值和射击速率和平均值和平均值相关联。对于由Cauchy White噪声或Cauchy-Lorentz分布的输入电流驱动的神经元，我们将Cestnik和Pikovsky [Arxiv：2207.02302（2022）]改编结果，并表明，对于任意初始条件，集体动力学将集体动力学降低到六个尺寸。我们还证明，在这种情况下，动力学渐近地收敛到Ott和Antonsen首先发现的二维不变歧管。对于相同的，无噪声的神经元，动力学将减少到三个维度，相当于渡边 - 斯特罗盖茨的描述。我们通过在可行的情况下计算不同渐近状态的非平凡盆地来说明在不变层之外的确切六维动力学。
We consider large networks of globally coupled spiking neurons and derive an exact low-dimensional description of their collective dynamics in the thermodynamic limit. Individual neurons are described by the Ermentrout-Kopell canonical model that can be excitable or tonically spiking, and interact with other neurons via pulses. Utilizing the equivalence of the quadratic integrate- and-fire and the theta neuron formulations, we first derive the dynamical equations in terms of the Kuramoto-Daido order parameters (Fourier modes of the phase distribution) and relate them to two biophysically relevant macroscopic observables, the firing rate and the mean voltage. For neurons driven by Cauchy white noise or for Cauchy-Lorentz distributed input currents, we adapt the results by Cestnik and Pikovsky [arXiv:2207.02302 (2022)] and show that for arbitrary initial conditions the collective dynamics reduces to six dimensions. We also prove that in this case the dynamics asymptotically converges to a two-dimensional invariant manifold first discovered by Ott and Antonsen. For identical, noise-free neurons, the dynamics reduces to three dimensions, becoming equivalent to the Watanabe-Strogatz description. We illustrate the exact six-dimensional dynamics outside the invariant manifold by calculating nontrivial basins of different asymptotic regimes in a bistable situation.
