论文标题
一些具有极限循环的最小双分子量质量表演系统
Some minimal bimolecular mass-action systems with limit cycles
论文作者
论文摘要
由于Feinberg，Berner，Heinrich和Wilhelm，我们讨论了三个具有三个物种的双分子质量成分系统的例子。每个系统都有一个独特的正平衡，对于某些速率常数而言不稳定，然后表现出稳定的极限周期，但没有混乱的行为。对于Feinberg的某些速率常数 - 伯纳系统，稳定的平衡，不缩小的极限周期和稳定的极限周期共存。从某种意义上说，这三个网络都是最小的。 通过同质化以上三个示例，我们构建了双分子质量质量的质量表演系统，四个物种接受了稳定的极限周期。同质化的Feinberg-伯纳系统和同质化的Wilhelm-Heinrich系统承认稳定平衡，不稳定的极限周期和稳定的极限周期的共存。
We discuss three examples of bimolecular mass-action systems with three species, due to Feinberg, Berner, Heinrich, and Wilhelm. Each system has a unique positive equilibrium which is unstable for certain rate constants and then exhibits stable limit cycles, but no chaotic behaviour. For some rate constants in the Feinberg--Berner system, a stable equilibrium, an unstabe limit cycle, and a stable limit cycle coexist. All three networks are minimal in some sense. By way of homogenising the above three examples, we construct bimolecular mass-conserving mass-action systems with four species that admit a stable limit cycle. The homogenised Feinberg--Berner system and the homogenised Wilhelm--Heinrich system admit the coexistence of a stable equilibrium, an unstable limit cycle, and a stable limit cycle.
