用两群耦合细胞设计相空间中的异宿可激发网络
Designing heteroclinic and excitable networks in phase space using two populations of coupled cells
摘要：
我们给出了一个建设性的方法来实现一个任意有向图（没有一个周期）作为一个异宿或可激发的动态网络的相空间中的两种类型的耦合细胞系统。在每种情况下，系统被表示为一阶微分方程系统。其中一种细胞类型（$p$ -细胞）通过相互抑制相互作用，并对我们当前接近的顶点（状态）进行分类，而另一种细胞类型（$y$ -细胞）选择性地激发$p$ -细胞，并仅在顶点之间存在过渡时才变得活跃。我们展示了开放的参数值集，这些动态网络的存在，并通过数值模拟表明，它们可以吸引适当选择的参数。
英文摘要：
We give a constructive method for realizing an arbitrary directed graph (with no one-cycles) as a heteroclinic or an excitable dynamic network in the phase space of a system of coupled cells of two types. In each case, the system is expressed as a system of first order differential equations. One of the cell types (the $p$-cells) interacts by mutual inhibition and classifies which vertex (state) we are currently close to, while the other cell type (the $y$-cells) excites the $p$-cells selectively and becomes active only when there is a transition between vertices. We exhibit open sets of parameter values such that these dynamical networks exist and demonstrate via numerical simulation that they can be attractors for suitably chosen parameters.
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