Ladenbauer Josef, Lehnert Judith, Rankoohi Hadi, Dahms Thomas, Schöll Eckehard, Obermayer Klaus
Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Marchstraße 23, 10587 Berlin, Germany and Bernstein Center for Computational Neuroscience Berlin, Philippstraße 13, 10115 Berlin, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Oct;88(4):042713. doi: 10.1103/PhysRevE.88.042713. Epub 2013 Oct 31.
We analyze zero-lag and cluster synchrony of delay-coupled nonsmooth dynamical systems by extending the master stability approach, and apply this to networks of adaptive threshold-model neurons. For a homogeneous population of excitatory and inhibitory neurons we find (i) that subthreshold adaptation stabilizes or destabilizes synchrony depending on whether the recurrent synaptic excitatory or inhibitory couplings dominate, and (ii) that synchrony is always unstable for networks with balanced recurrent synaptic inputs. If couplings are not too strong, synchronization properties are similar for very different coupling topologies, i.e., random connections or spatial networks with localized connectivity. We generalize our approach for two subpopulations of neurons with nonidentical local dynamics, including bursting, for which activity-based adaptation controls the stability of cluster states, independent of a specific coupling topology.
我们通过扩展主稳定性方法来分析延迟耦合非光滑动力系统的零延迟和簇同步，并将其应用于自适应阈值模型神经元网络。对于兴奋性和抑制性神经元的均匀群体，我们发现：（i）阈下适应使同步稳定或不稳定，这取决于循环突触兴奋性或抑制性耦合是否占主导；（ii）对于具有平衡循环突触输入的网络，同步总是不稳定的。如果耦合不太强，对于非常不同的耦合拓扑结构，即随机连接或具有局部连接性的空间网络，同步特性是相似的。我们将我们的方法推广到具有不同局部动力学的两个神经元亚群，包括爆发，其中基于活动的适应控制簇状态的稳定性，而与特定的耦合拓扑无关。
