arXiv:2607.14143math.DScs.AI2026-07
证明了平面系统中正环是多稳态的必要条件。
The Planar Case of Thomas Positive Circuits Conjecture
- 用平面动力系统方法分析正环存在性
- 给出平面系统满足托马斯猜想的充分条件
- 适合研究生物网络与系统动力学的学者
电路描述动力系统中元素间的循环定向影响，分为正环和负环。R. Thomas提出，多稳态存在的必要条件是系统中存在正环。本文利用动力系统工具和平面分析，研究平面系统中该猜想成立的条件，明确了正环在平面系统多稳态中的关键作用。
原文摘要 · Abstract (English)
The notion of circuit refers to a cyclic oriented influence between the elements of a dynamical system. There are two classes of circuit: positive and negative. R. Thomas conjectured that a necessary condition of multi stationarity is the existence of positive circuits. In this paper we use dynamical system tools and planar analysis to find conditions for which the conjecture holds for planar systems.
动力系统多稳态生物网络
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