Limit cycles in mass-conserving deficiency-one mass-action systems
Limit cycles in mass-conserving deficiency-one mass-action systems
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DOI：
10.14232/ejqtde.2022.1.42
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发表时间：
2022-01-01
影响因子：
1.1
通讯作者：
Hofbauer, Josef
中科院分区：
文献类型：
--
作者：
Boros, Balazs;Hofbauer, Josef
我们给出了一些简单的质量作用系统，它们的极限环都在亏一定理的范围内。所有构造的例子都是质量守恒的，并且它们的化学计量子空间是二维的。利用连续化软件MATCONT，我们同时描绘了所有化学计量类的极限环。这些网络是三分子和四分子的，有些网络表现出两个甚至三个极限环。最后，我们证明了具有二维化学比量子空间的双分子反应网络的关联质量作用系统不存在极限环。
We present some simple mass-action systems with limit cycles that fall under the scope of the Deficiency-One Theorem. All the constructed examples are mass -conserving and their stoichiometric subspace is two-dimensional. Using the continua-tion software MATCONT, we depict the limit cycles in all stoichiometric classes at once. The networks are trimolecular and tetramolecular, and some exhibit two or even three limit cycles. Finally, we show that the associated mass-action system of a bimolecular reaction network with two-dimensional stoichiometric subspace does not admit a limit cycle.