几乎完全和相等的异宿网络
Almost complete and equable heteroclinic networks
摘要：
异宿连接是一种连接自治动态流的不变集的轨迹：对于具有流不变空间的系统，这些连接可以在平衡点之间鲁棒地形成网络。在本文中，我们研究了作为流不变集的异宿网络和节点之间可能连接的有向图之间的关系。我们考虑实现的一大类传递有向图作为强大的异宿网络，并表明，虽然强大的实现通常是不完整的（即不是所有的节点的非稳定流形的一部分的网络），他们可以几乎是完整的（即完整的一套零措施内的非稳定流形）和均衡的（即所有的连接从一个节点具有相同的尺寸）。我们表明，有几乎完全和平等的实现，可以通过添加一些额外的节点和连接关闭。我们讨论了一些例子，并描述了一个意义上的一个均匀的几乎完全网络嵌入是一个最佳的描述随机扰动运动的网络。
英文摘要：
Heteroclinic connections are trajectories that link invariant sets for an autonomous dynamical flow: these connections can robustly form networks between equilibria, for systems with flow-invariant spaces. In this paper we examine the relation between the heteroclinic network as a flow-invariant set and directed graphs of possible connections between nodes. We consider realizations of a large class of transitive digraphs as robust heteroclinic networks and show that although robust realizations are typically not complete (i.e. not all unstable manifolds of nodes are part of the network), they can be almost complete (i.e. complete up to a set of zero measure within the unstable manifold) and equable (i.e. all sets of connections from a node have the same dimension). We show there are almost complete and equable realizations that can be closed by adding a number of extra nodes and connections. We discuss some examples and describe a sense in which an equable almost complete network embedding is an optimal description of stochastically perturbed motion on the network.
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