一类反应网络及其多项式动力系统
On classes of reaction networks and their associated polynomial dynamical systems
摘要：
在研究反应网络及其生成的多项式动力系统时，已经识别出具有重要性质的特殊网络类别。这些网络包括可逆网络、弱可逆网络以及最近的趋内网络。虽然这些网络类型之间的一些包含是清楚的，例如所有可逆网络都是弱可逆的，但其他关系更加复杂。增加这种复杂性的是，包含物可能处于由网络产生的动力系统的水平，而不是网络本身的水平。我们完整地描述了可逆，弱可逆，内规和强内规网络之间的包含体，以及其他研究较少的网络类型。特别地，我们证明了每个二维强内趋网络都可以由一个极弱可逆网络生成。我们还介绍了一类新的只有源的网络，这是一个计算方便的网络属性，并显示如何将这一类与上述网络类型。
英文摘要：
In the study of reaction networks and the polynomial dynamical systems that they generate, special classes of networks with important properties have been identified. These include reversible, weakly reversible}, and, more recently, endotactic networks. While some inclusions between these network types are clear, such as the fact that all reversible networks are weakly reversible, other relationships are more complicated. Adding to this complexity is the possibility that inclusions be at the level of the dynamical systems generated by the networks rather than at the level of the networks themselves. We completely characterize the inclusions between reversible, weakly reversible, endotactic, and strongly endotactic network, as well as other less well studied network types. In particular, we show that every strongly endotactic network in two dimensions can be generated by an extremally weakly reversible network. We also introduce a new class of source-only networks, which is a computationally convenient property for networks to have, and show how this class relates to the above mentioned network types.
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